Golfweek and The Golf Channel reported the six players on the tour policy board, which must approve any final deal on the PGA-PIF merger framework unveiled last June, were being encouraged to meet with Al-Rumayyan at Ponte Vedra Beach, Florida - site of this week's Players Championship.
Joining Woods among those on the board are fellow Americans Patrick Cantlay, Jordan Spieth, Peter Malnati and Webb Simpson plus Australian Adam Scott.
Golfweek called the gathering an "icebreaker" in a bid to speed up the talks, which have extended beyond an original December deadline, to unite the PGA and the financial backers of the upstart LIV Golf League.
"We're being encouraged to potentially meet with them, but at the same time we probably feel like our membership should know the timing and what could happen and just, in general, maybe it's just a meet," Spieth told reporters after his second round at the Players on Friday.
"We're being encouraged, obviously, which I think is probably a good thing that the entire board should if there's going to be any potential for a negotiation."
The six players are also on the board of directors for the new PGA Tour Enterprises, the for-profit arm formed in a merger with the US team sport owners of Strategic Sports Group (SSG), which invested $1.5 billion into the new venture.
That Enterprises board reportedly is set to meet at Ponte Vedra Beach on Tuesday.
"If the PIF thinks it's beneficial, we meet and I think it's a good thing to do," Scott told Sports Illustrated. "As far as getting on with business, let's get on with business.
"I'm curious to see how it all pans out just like everyone in the game," Scott told Golfweek. "I'm as curious as I was to meet any of the (Enterprises) investor groups last year, just to put a face to a name and hopefully see that everyone is going into this with the right intent."
Need all input possible
The Saudi PIF, which could become an investor into PGA Tour Enterprises, has pumped billions of dollars into supporting LIV Golf, whose rich money deals and lighter schedule have enticed several big names from the PGA to play in the breakaway tour, including reigning Masters champion Jon Rahm and 2023 PGA Championship winner Brooks Koepka.
Scott said meeting with Al-Rumayyan would be logical as players decide whether or not to accept financing from the largest sovereign wealth fund in the world or reject it and likely keep the sport's top talent divided.
"Ultimately, the players vote going into whether a deal will happen or not, just like it was with SSG last year," Scott said.
"And with the seriousness of what we're voting on, I think it's important that we've all met and no matter what anyone's feelings are, I think when you're voting on these things, you can't be completely blind and need to have all the knowledge and input possible to make the best decisions."