Imagine this: Sunday at Hazeltine. Ryder Cup on the line. Match play. Mickelson versus Stenson.

“That would be awesome,” Davis Love III, captain of Ryder Cup USA, said Monday, a day after Swede Henrik Stenson edged out American Phil Mickelson in an epic duel to win the British Open Championship in Scotland.

“It would be a battle we remember forever, and I’m sure Phil would like another shot at Henrik, as well,” Love said in an interview posted on PGA.com.

Following their showings at Royal Troon golf course last week, both Mickelson and Stenson appear to have secured positions on their respective teams for the Ryder Cup, which will be played this fall in Minnesota.

Golf’s biggest team competition, pitting Europe against the United States, will be held Sept. 27 to Oct. 2 at Hazeltine National Golf Club in Chaska.

The odds of a Royal Troon repeat are remote; pairings for the 12 head-to-head matches on the Ryder Cup’s final day are determined randomly.

As a 46-year-old veteran of 10 Ryder Cups, Mickelson’s presence would be expected to include not just golf skill, but wisdom for the event, which features raucous crowds and team jubilance not witnessed anywhere else in professional golf. Love described Mickelson as “one of the best leaders in the world.”

But Mickelson isn’t the only veteran with potential to play.

Vice captain Jim Furyk (age 46; 9 Ryder Cup appearances) who finished runner-up at the U.S. Open, sits 19th in the rankings to make the team, and fellow vice captain Steve Stricker vaulted from 49th to 22nd after a fourth-place finish at Royal Troon.

Here’s what Love had to say about Stricker, a 49-year-old Wisconsin native who has played in four Ryder Cups:

“Steve is one of the guys that I respect the most late in his career. He’s a part-time golfer right now. He’s doing what’s best for his family, his body and his outlook, but he plays great when he plays. He plays when he wants to and how he wants to.

“Steve turns down an awful lot of money to do it his way. Bruce Lietzke did it that way, too. As the captain, I have to factor that in when I look at the points. Steve has played in half the events as most of the other guys, and he’s No. 23 right now. Look what he’s done in his body of work. That’s some great golf, and it puts me in a spot where I have to think about him — especially with guys like Brooks Koepka and Daniel Berger battling injuries right now. What’s best for the team?

“It’s going to be interesting with the PGA next week. How much will Strick play after that? That’s why it’s so nice to have all the vice captains we have and advisers we have. Phil said he’d make the team, and he probably has on points. So he’s someone that Tom Lehman, Tiger Woods (two other U.S. vice captains) and me will be talking to.

“If anything, I think it might narrow down the conversations a little — with the way Jim and Steve have been playing, we can leave them out of the conversation, and I can just talk to Tom and Tiger about it.