Mickelson stoked the flames, saying he would welcome the chance to play with his old foe.
But today USA captain Jim Furyk admitted the chances were unlikely, but not impossible.
“I guess nothing’s out of the realm,” he said today.
“They did play some golf yesterday. I think they both mentioned it would be a lot better pairing than it was in the past.
“You know, I won’t ever say it wouldn’t happen, but it’s probably not too likely.”
Woods and Mickelson were put together in 2004 at Oakland Hills and didn’t click – failing to win a point on the opening day.
They’ve had a long-running rivalry which will come to a head later this year in a high-stakes contest between the two.
And Furyk admits he’s got to be careful pairing some personalities together.
“I wouldn’t say that anybody could be with anybody, on both sides,” he said. “It’s not that guys don’t get along. Rarely do you see two really fiery guys paired together or two real complacent guys paired together.
“Bernhard Langer, one of my favourite guys, but you might not pair him together with himself because they are just even keel. You pair him with a guy that’s feisty, a Seve, and you kind of get the ham-and-egg effect of things.
“One of the tasks for every captain is really trying to figure out how you get a depth of strength so you feel like at each session you have four great groups out on the course.
Woods’ former coach Butch Harmon admits America have often found it tough to pair someone with him.
He said: “Talking to a lot of American players, they have often struggled being Tiger’s partner. It’s not so much that Tiger has played poorly in Ryder Cups, the guys often say how they tried too hard because they didn’t want to let him down.
“If you look at all the combinations they had, because they seemed to try most players on the various teams, I think Tiger played fine but he just didn’t get any help.
“It went wrong when Phil Mickelson played with Tiger in 2004 because in those days, they barely talked to each other. They lived separate lives in different parts of the country and didn’t really play any practice rounds together.
“In those days, if you put Woods and Mickelson together then you ruined two other teams. At that point in time that was a disaster not only in the morning, but they put them out again the afternoon which I really didn’t understand.
“If you put them together now, which I hope they don’t because I think you take away two teams, I think it might work now as they get along fine. This has the potential to be the most exciting Ryder Cup ever.”
But yesterday, after a practice round together, Mickelson appeared to hint a shock pairing was on the cards.
“I think we would both welcome it,” Mickelson said. “And I do have an idea of what captain Furyk is thinking, yeah.”