Al-Rumayyan co-founded LIV in 2021 and has been the tour’s most powerful figure.
This week LIV postponed its June event in New Orleans, meaning it will not have any tournaments in the US between 10 May until 6 August, when it goes to Trump Bedminster in New Jersey.
BBC Sport has been told LIV remains hopeful of remaining an international tour with a team model, and that it is in “constructive” talks with potential investors.
Sources indicated that executives are exploring a number of opportunities to “reposition” the business. They said LIV Golf was on course to earn $100m (£86m) more in 2026 than last season.
But officials accept it is likely the series will have to be significantly scaled back, with far fewer events.
Team captains have been warned that the company will reveal plans to find new financial backers on Thursday.
LIV declined to comment.
This month LIV Golf chief executive Scott O’Neil told players the 2026 season would continue “as planned and uninterrupted” amid rumours the tour was on the verge of collapse, although he did not address what might lie ahead.
It came as PIF announced a new strategy, with a focus on more sustainable investments.
The LIV project, which pivoted to a more traditional 72-hole format this year, has been bankrolled by an eye-watering amount of money from PIF.
Major winners Jon Rahm, Bryson DeChambeau, Phil Mickelson and Cameron Smith are among the players who compete on the tour.
The overall investment surpassed $5bn (£3.8bn) when fresh capital of $267m (£229m) was injected this year.
The tour’s net losses in markets outside the US increased to $462m (£340m) in 2024, meaning it had lost more than $1.1bn (£810m) since it was established in 2021.
With vast amounts of money pumped into the US arm of the operation, losses look likely to run to several billion dollars.
PIF has been approached for comment.