Admittedly, they've had a tough time coming through qualifying, and will need to beat New Zealand in a play-off - but it still makes for one of the strangest tales we've heard in a long time.
It got The Rundown thinking about some of the stories of the strangest football clubs from around the world - so here's our pick of some of those tales, starting with the Mexicans themselves:
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Tokyo residents on their expectations for the Olympic Games in Japan
Mexican national team
Mexico's near-disastrous World Cup qualifying campaign has now seen four changes of manager in the past six weeks. They only earned a play-off spot when the USA did them a massive favour by scoring two late goals against Panama in the final qualifying match. The Mexicans, who were in control of their own fate, lost 2-1 to Costa Rica the same day. Mexico will take on New Zealand for a place in the tournament itself with a new coach, Miguel Herrera, at the helm.
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If you think Mexico is bad for switching managers, spare a thought for the men who've been tasked with running Sicilian Serie A side Palermo by club owner Maurizio Zamparini. In 2011 alone, the club had Delio Rossi, Serse Cosmi, Delio Rossi (again), Stefabo Piolo, Devis Mangia and Bortolo Mutti as manager. The second of Rossi's stints that year lasted less than one day.
Since Zamparini took over the club in the summer of 2002, there have been 26 changes of manager. But what we REALLY can't get over is how Zamparini has managed to persuade five men (Delio Rossi, Gian Piero Gasperini, Giuseppe Sannino, Francesco Guidolin and Stefano Colantuono) to take the job on more than one occasion. Guidolin alone has had four separate spells in charge!
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When Ken Richardson took over the club in the 1990s he talked up Rovers' chances of glory. Instead, he ended up trying to burn down the stadium.
Richardson lost interest in the club after being refused planning permission for a new stadium and hired three thugs to burn down the ground so he could claim on the insurance. They failed, Richardson was jailed for four years for his attempted fraud, and Doncaster ended up being relegated from the football league with a -83 goal difference.
The club barely survived, but has since been saved - and ironically now has the new stadium that Richardson was after in the first place.
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The hugely popular Brazilian team was led by international superstar Socrates, and from 1982 to 1984 went through a spell in which the star player did great justice to his ancient Greek namesake. In protest at the military dictatorship running the country at the time, the players took over the decision-making at the club on a purely democratic basis, holding aloft a banner reading "Win or lose, always with democracy" whenever they came onto the pitch. It worked on the pitch, but not off it: Corinthians won back-to-back Sao Paolo championship titles in 1982 and 1983, but a parliamentary motion to force a return to democracy failed, and the military dictatorship continued.
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The Italian side went through the entire 1978-79 Serie A season without losing a match, the first team ever to do so in the Italian top flight - yet somehow managed not to win the Scudetto. They were pipped by AC Milan, thanks in large part to a staggeringly negative approach which saw them draw 12 of their 15 away matches in the season.
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Every single team in Andorra
Every single one of the teams in Andorra share two stadiums, with every match in both the divisions taking place at either the Estadi Comunal d'Andorra la Vella, which has real grass, or the Camp d’Esports d’Aixovall, which used to have grass but is now covered in astroturf. The two pitches in the tiny, mountainous principality (which is roughly 13 miles across and has a population of just 78,000) host every game in the two football leagues, the Constitution Cup, the Andorran Super Cup (seriously) and the play-offs. They also use the same pitches for Andorra's two rugby teams.
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The Roman giants had an all-conquering side in the early 1970s spearheaded by the legendary Giorgio Chinaglia, and they won the title in 1974. There was only one problem: the players couldn’t stand each other, loathing each other so fiercely that the club had to set up an extra dressing room so that the two factions among the players could be kept separate. Chinaglia described training matches between the two different factions as, "all out war… but then on a Sunday everybody used to pull for each other."
That's just the start of the strangeness: the team was struck by one of the most notorious curses in Italian sport. Coach Tommaso Maestrelli died of cancer at the height of his powers, midfielder Luciano Re Cecconi was shot and killed while pretending to rob a jewellers' shop as a joke, and another midfielder, Mario Frustalupi, was later killed in a car crash.
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In November 2007, the Conference side was taken over by an internet-based firm called MyFootballClub, which demoted previous manager Liam Daish to the status of first team coach and allowed fans to make all the decisions in the club - including team selection for each match - by paying £35 for a share in the club and then voting online. 27,000 fans signed up - no doubt buoyed by great experience playing Championship Manager - to take part, but the experiment proved a dismal failure. The number of members paying their £35 subscriptions dropped to just 3,500, the club got relegated, and the members eventually voted to hand Ebbsfleet over to the Fleet Trust, a supporters' trust set up to save the club.
Not strange enough for you? Then try this: Kelsey 'Frasier Krane' Grammer is the brother-in-law of Ebbsfleet striker Phil Walsh, and the Hollywood A-lister is a regular sight in the stands when he's visiting with his air hostess wife Kate.
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Queen's Park FC
The Glasgow club is one of the most bizarre sporting entities in the world: despite average league attendances of around 750, they play at Hampden Park, which seats over 52,000 and was the largest stadium in the world until the Maracana was built in Rio for the 1950 World Cup.
But that's not why they make this list. That honour is bestowed because of their exploits in the 1872 FA Cup south of the border. As the top team in Scottish football at the time they decided to enter the English FA Cup, and made it as far as the semi-finals without kicking a ball, as team after team pulled out of the tournament. They earned a 1-1 draw in the semi-final against Wanderers, but couldn't afford the train fares to come south again for the replay. Wanderers were awarded a bye into the final, and went on to win.
Queen's Park gave it another go in subsequent years, and made the final in both 1884 and 1885 - the only Scottish side ever to do so - but both times lost to Blackburn Rovers.
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The Russian side set an extraordinary record as they made it to the final of the Russian Cup in 2011 without scoring a goal. As a Russian Premier League side they entered the tournament in the last-32, and came through their first two matches on penalties after 0-0 draws with Kamaz Naberezhnye Chelny and Gornak Uchaly respectively. They then received a bye into the semi-finals as FC Saturn Moscow Oblast went bankrupt during the winter break, then they won another shoot-out in the semi-final against Rostov.
They broke their goal drought in the final with Brazilian striker Neco scoring in the 23rdminute - their first goal in 383 minutes of Cup football - but ended up losing 2-1 to CSKA Moscow.
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There are plenty of other teams we could have mentioned: Steaua Bucharest in the Ceausescu dictatorship era in Romania, or Arsenal's bizarre years from 2007 to 2012 in which they tried to win the Premier League and Champions League by repeatedly selling their best player each summer.
You've probably got your favourites, too: share them with the world in the comments box below...
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