The Irishman has been a Vice Captain in the last three Ryder Cups
Rose Calls Padraig Harrington "Front Runner" For Ryder Cup Captaincy
"I would say that Padraig, for me, would be the front-runner," Rose said.
"I would say as a three-time major champion, and clearly a European legend, Padraig is the front-runner, but you've also got Lee Westwood.
Related: Who will be European Ryder Cup Captain in 2020?
"It's interesting when you try to project out who the possible captains are for the next 10 Ryder Cups.
"But if Padraig doesn't do it this time then I'm not sure, you have got to start fitting guys in.
Harrington made six Ryder Cup appearances as a player and has been a Vice Captain at the past three matches.
The three-time major winner tasted victory in the Ryder Cup in four of his six appearance and won 10.5 points from 25 games.
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Justin Rose isn't the only European backing Harrington for captaincy, Rory McIlroy is as well.
"I've always thought Padraig would be a good captain in the United States," the four-time major winner said last week.
Related: Who will be USA Ryder Cup Captain in 2020?
"He's won a lot of golf tournaments over there, including a [US] PGA Championship.
"I think the continuity in the European camp having all these vice-captains this year and preparing for captaincy down the road has been a huge foundation of why we've been so good."
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