Mickelson told Golf.com about the matchup on Thursday, saying that negotiations are still underway. Mickelson also said that the matchup was originally planned for July 3 in Las Vegas and was a primetime TV special.
The negotiations also involve a major television network and several corporate entities, according to the report.
"We're working on a different date," Mickelson told Golf.com. "I thought it was done for the 3rd but obviously it wasn't."
Woods and Mickelson teased the idea of a head-to-head duel at the Players Championship, saying they would both support a winner-take-all head-to-head setup.
Mickelson has five major titles, while Woods has 14 majors. Woods' last major championship came in 2008, while Mickelson won his last in 2013.
The duo teamed up for a practice round in April at the Masters.
"We had so much fun," Mickelson told ESPN. "He's a fun guy to be around. We had a great time. We partnered up."
Mickelson said the biggest point for him and Woods was when they came together to help win the 2016 Ryder Cup.
They were paired together for the first two rounds of the Players Championship.
"The excitement that's been going on around here, it gets me thinking: 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 told reporters at the Players Championship.
"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."