The Englishman, who has been on the winning side on eight different occasions in the competition, revealed that he would much prefer to captain Europe in 2022 in Italy.
"I won't put my name forward for this one. I'd prefer to do it if Rome in possible," Westwood told Sky Sports.
The former world No.1 was one of the vice-captains in this year's Ryder Cup where Europe secured an emphatic victory over the United States to regain the trophy in France.
Westwood believes that fellow Ryder Cup vice-captain Harrington should be the one to lead the Europeans into the next tournament.
"I think Padraig is a better candidate for the next one than me and we need to pick the best man for the job," he said.
"He is the right age and he's still in touch with the players because he's still playing out here."
Harrington has featured in six Ryder Cup teams and he has been the vice-captain three times.
Thomas Bjorn, who captained Europe to victory this year, also stated that Harrington is the favourite to lead out the team in Wisconsin in two years' time.
"I've always said when you've got somebody that's a three-time major champion and has the pedigree that Padraig has and holds the respect of the players that he does, it would be difficult to see him not doing it at some stage," he said.