PONTE VEDRA, BEACH, Fla. — This could be fun.

Tiger Woods and Phil Mickelson paired together for the first two rounds of the Players Championship this week at TPC Sawgrass marks the first time the two will play in the same group since the 2014 PGA Championship.

So Mickelson began Tuesday playfully calling out Woods, wondering aloud if Woods “wants a piece of me.’’

“Why don’t we just bypass all the ancillary stuff of a tournament and just go head to head and just have kind of a high-stakes, winner-take-all match?’’ Mickelson said, sharpening his needle directed to the side of Woods.

“Now, I don’t know if he wants a piece of me, but I just think it would be something that would be really fun for us to do, and I think there would be a lot of interest in it if we just went straight to the final round.’’

Woods and Mickelson have played in the same group 36 times on the PGA Tour, with Woods shooting the lower score 16 times, Mickelson besting Woods 16 times and four ties. Mickelson, however, has had the better of the more recent play, with an 8-5-1 record against Woods since 2007.

“Fifteen years ago my record against him sucked,’’ Mickelson said. “And now it’s OK.’’

About five hours after Mickelson spoke, Woods responded to the “does he want a piece of me’’ salvo.

“Well, first of all … big picture,’’ Woods said with a smirk, a reference to his 79 career victories, including 14 major championships, to Mickelson’s 43 and five. “How many times have we won on Tour?’’

Where there once was some jealousy and tension between Woods and Mickelson when Woods was breaking opposing players’ wills on a weekly basis with his sheer dominance, there now is mutual respect and friendship, built and fostered during the recent Ryder Cup and Presidents Cup competitions, when Woods served as an assistant captain because of his back injuries.

When Woods was sidelined with his back issues, Mickelson would text him encouraging messages. When Woods was mired with the chip yips in 2015, Mickelson reached out and offered advice on chipping.

At the Masters last month, the two played a practice round together that drew as much fan and media attention as the final round of a tournament might.

“It’s going to be fun playing with him again,’’ Woods said. “We have both done this throughout our careers. We have always looked at each other and said, ‘Where is he on the board?’ That’s what Arnold [Palmer] and Jack [Nicklaus] used to do all the time.’’

Their fellow players — most notably Rickie Fowler, the third player in the group — will have their eyes glued to the Woods-Mickelson subplot.

“I’ve got the best seat in the house,’’ Fowler said.

“I play early Thursday, so I’ll probably be on the couch in my hotel room watching that one in the afternoon,’’ Justin Thomas said. “It’ll be cool to watch them play.’’

Mickelson said the young players like Thomas, Fowler, Jordan Spieth et al have little idea of how good Woods was when he was at his peak.

“I don’t think anybody today who wasn’t there that witnessed it, and I don’t think anybody before, will ever see that level of play again,’’ Mickelson said. “It was the most remarkable golf in the history of the game, and I think unrepeatable. I think it was that good.

“I look at 2000 as being kind of the benchmark at the U.S. Open as being the greatest golf I’ve ever witnessed, and I believe ever has been played. And it sucked to have to play against him. It really did. You look at it, and you say, ‘How am I going to beat this?’ ’’

The last time Woods and Mickelson were paired together at the Players Championship was in 2001, when Woods won and was at the height of his dominance.

“It’s been four years since we’ve been paired last on Thursday-Friday, and I don’t think we should wait for the governing bodies to put us together,’’ Mickelson said. “I think we should just do something on our own and get after it.’’

When Woods was asked whether he’d be up for Mickelson’s winner-take-all proposition, he said, “I’m definitely not against that at all. We’ll play for whatever makes him feel uncomfortable.’’

Asked what that might be, Woods responded, “We’ll find out.’’