Woods fired a 3-over 74 during Sunday's final round of the Wells Fargo Championship.
Mickelson believes no one will eclipse the golf Woods played in compiling 14 major titles, the most recent coming at the U.S. Open 10 years ago.
"First of all, big picture", Woods said as his smile widened. "We are normally paired up on the weekend if we are both playing well, and even that's a rarity".
"We don't really get paired together", Woods said. We always have. But I think our relationship has certainly gotten a lot closer with me being a [Presidents Cup and Ryder Cup] vice-captain the last couple teams, and sitting there and having very lengthy conversations with him about things. "Now, I don't know if he wants a piece of me", he cracked to laughter, "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".
"I've learnt to love it, to like it". Towards the beginning part where my back got bad, we started getting on the same side of the draw but not in the same groupings.
Mickelson is a five-time major victor, but didn't collect his first until the 2004 Masters.
A two-time victor of an event dubbed the unofficial fifth major, Woods will be in the field for the first time since 2015 when he tees off alongside Phil Mickelson and Rickie Fowler on Thursday. Mickelson had a two-stroke lead going into the last day but Woods shot 66 to Mickelson's 69 to win by one. From 1997 to 2013, he won 79 PGA Tour events, which is second all-time behind Sam Snead's 82 wins. Although he had back-to-back birdies on the seventh and eighth holes, his momentum was stalled by a bogey on the 11th - when his tee shot finished in a fairway bunker - and then another on the 14th, where he drove into the water hazard and had to take a penalty drop before rescuing a bogey five.
Mickelson, a 47-year-old left-hander, owns five major titles and has 43 US PGA triumphs.
Mickelson had earlier offered effusive praise of just how powerful Woods was in his prime. It's fun for me to be able to have an opportunity to play with Phil the first two days.
"It was the most remarkable golf in the history of the game, and I think unrepeatable".
Mickelson won the Players in 2007, and Fowler won it in a playoff in 2015.
Rory McIlroy is also in Featured Group coverage, playing alongside three-time major victor Jordan Spieth and FedExCup champion Justin Thomas in the early part of the week.