Coleman said after guiding Wales to the semi-finals of Euro 2016 that the 2018 World Cup campaign would be his last in charge.
But assistant boss Osian Roberts raised the possibility of Coleman remaining in a job he has filled since January 2012 after the 1-1 draw with Serbia in June.
Roberts said Coleman could "hopefully be persuaded to stay on" and former Wales striker Hartson does not rule his old team-mate having a change of heart.
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"People can always change their mind and I'm sure when Chris looks at his players he will realise what a great group he's got," Hartson told Press Association Sport.
"The top players he has - Gareth Bale, Aaron Ramsey and Joe Allen - are coming into their peak years now.
"These players will be in their late 20s in the next campaign and that's when they will be at their best.
"He's also got some good youngsters coming through, people like Tom Lawrence and Ben Woodburn, so there's a great blend of youth and experience.
"I hope Chris stays because he's done the most amazing job for Welsh football and the players absolutely love his honesty and professionalism.
"But whatever he decides I think people have to respect his decision. He has certainly earned that because of the job he has done."
Coleman will name his squad for the World Cup double-header against Austria and Moldova on Friday.
Neil Taylor misses Austria's visit to Cardiff on September 2 after the red-card tackle which broke the leg of Republic of Ireland captain Seamus Coleman in March.
But the Aston Villa full-back will be available for the trip to Moldova three days later.
Midfielder Joe Ledley is expected to be included despite being without a club since leaving Crystal Palace in June.
Unbeaten Wales are four points adrift of Group D front-runners Serbia and the Republic with four games left to play.
But Hartson believes there is cause for optimism after the Serbia draw, which was achieved without suspended talisman Bale.
"I feel we are due a bit of luck," Hartson said. "We've led in five of the six games in the group and we've been pegged back.
"I look at the fixtures and I think they're good for us.
"We've got the two toughest games, Austria and Ireland, at home and the two weakest teams, Moldova and Georgia, away.
" I really think we can win our last four games.
"But we are going to have to play well and counter well like we did in Euro 2016 qualification and at the tournament itself."
:: John Hartson was speaking at the McDonald's & Football Association of Wales Community Football Day in Berriew, celebrating 15 years of McDonald's partnering with the four UK home nations & supporting grassroots football. For more information visit www.mcdonalds.co.uk/betterplay
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