Only the nine group winners qualify automatically for the World Cup while the eight best runners-up will advance to a round of playoffs for the remaining four berths in Russia.
Bale said he wanted Coleman to remain in charge and help steer the side to Russia.
"What he has done for the team and Welsh football has been amazing," Bale told the Daily Telegraph.
"Qualification could have gone better but we're going to do everything we can to get there.
"It won't be easy and there's a lot we have to do in the group now but Chris is the man who can keep us focussed and positive and show us how to get the results we need."
Bale also said Wales had to move on from their Euro 2016 campaign, where they reached the semi-finals, and focus on World Cup qualification.
"We don't want to keep on looking back at the Euros. For everyone it was incredible to be a part of that and we all want that again," the Real Madrid winger added.
"It would mean everything to reach Russia -- we've only reached one World Cup finals before and that was back in the 1950s."
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by Peter Rutherford)
