The second leg of the final was called off twice at the weekend after the bus carrying the Boca team was attacked by rival fans outside River's Monumental stadium in Buenos Aires on Saturday, injuring several players.
The kickoff was initially delayed before the game was postponed from Saturday to Sunday. On Sunday, it was postponed again, hours before kickoff, after Boca said they were not in a fit state to play.
The South American football confederation CONMEBOL is due to meet both clubs on Tuesday to discuss rescheduling and the venue. The first leg at Boca's stadium ended 2-2.
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The Genoa city government confirmed in a statement on Monday that it had written to the clubs offering to host the game.
The Libertadores is South America's equivalent of Europe's Champions League and it is the first time two teams from the same city had reached the final.
River Plate – Boca Juniors
Image credit: Getty Images
"Deep, in fact, are the bonds that unite the two Argentine football clubs - both founded by Genoese immigrants at the beginning of the twentieth century - with the Ligurian capital," Genoa's government said.
The city's sports director Stefano Anzalone added: "We would be very proud to host important clubs like Boca and River in our city by welcoming them in what, in some ways, is also their first home.
"It would also be a further opportunity to give international visibility in Genoa at this time of difficulty and to renew the profound sense of friendship that historically unites us with those societies."
The city is still recovering from the accident in August when a motorway bridge collapsed, killing 43 people.
Boca are generally more closely associated with the city and are nicknamed the "Xeneizes", the local dialect's word for "Genoese".
River Plate's connections with the city are less well known although some versions of their history say the club adopted red and white as their colours because they are the same as Genoa's flag.
Midfielder plays in goal but River win in Copa Libertadores
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