That is after winning the backing of on-course leader Rory McIlroy.
The 47-year-old Irishman, who served as a vice-captain to Thomas Bjorn for Europe’s triumph at Le Golf National over the weekend, wants the job and McIlroy’s support should ensure he gets it.
“You need a certain type of captain in the United States, and a certain type of captain in Europe,” said McIlroy.
“And for me Padraig Harrington would be a great captain in the US because of his playing record and because everyone over there likes him.
“Padraig has a connection with the fans over there and he has won US PGA Championships and won there a few times.
“The great thing about European sides is the continuity and the fact that the vice-captains play a role a few years in advance of taking the captaincy so they are prepared for it.
“Thomas did it for a while and was a great captain.”
Harrington has been a vice-captain for the past three Ryder Cups.
Taking the main role in Wisconsin would see him line up against home-state boy Steve Stricker.
“I’d love to be a Ryder Cup captain. I’d love to bring my thoughts to the game,” Harrington said.
“But it’s an interesting one because I wouldn’t do it without a certain amount of trepidation.
“It’s a tough, tough job. Unfortunately, the captain gets judged on results rather than anything else. I wouldn’t go into it lightly, but on balance, yes I want to be a Ryder Cup captain.”
Bjorn, who has yet to decide if he wants to be part of the next captain’s backroom staff, is behind Harrington’s bid.
“He’d be brilliant. He’s got all the tools and all the knowledge,” said the Dane.
A five-man committee including the three most recent Ryder Cup captains, European Tour chief executive Keith Pelley and a players’ representative is expected to make the appointment in December.