Al-Rumayyan co-founded LIV in 2021 and has been the most powerful person on the tour.
This week LIV postponed its June event in New Orleans, meaning it will have no tournament in the US between May 10 and August 6, when it will take place at Trump Bedminster in New Jersey.
However, LIV tournaments are scheduled to take place in South Korea, Spain and the UK during this period.
BBC Sport has been told that LIV is hopeful of maintaining an international tour with a team model and is in “constructive” talks with potential investors. The series is said to be “completely up for sale”.
Sources indicated that officials are exploring several opportunities to “rehabilitate” the business. He said LIV Golf was on track to earn $100m (£86m) more in 2026 than last season.
But officials acknowledge that it is possible the series will have to be scaled down significantly, at most, to fewer than the current 14 events.
Team captains and staff have been informed of LIV’s plan to find new funding.
LIV declined to comment.
This month LIV Golf chief executive Scott O’Neill told players the 2026 season would continue “as planned and uninterrupted” amid rumors the tour was on the verge of collapse, although he did not specify what might happen next.
It came as PIF – which also owns Premier League club Newcastle United – announced a new strategy with a focus on more sustainable investment.
Major winners Jon Rahm, Bryson DeChambeau, Phil Mickelson and Cameron Smith are among the players who compete on the LIV Tour.
The project, which this year is based on a more traditional 72-hole format, has been financed by a surprise sum of money from the PIF.
Total investment surpassed $5bn (£3.8bn) this year when $267m (£229m) of new capital was injected.
The Tour’s net losses in markets outside the US rose to $462m (£340m) in 2024, meaning it has lost more than $1.1bn (£810m) since its inception in 2021.
But given the huge sums of money invested in the US branch of the operation, overall losses are likely to reach several billion dollars.
In February, Rahm, Smith and DeChambeau turned down a one-time opportunity to apply for reinstatement to the PGA Tour under its ‘Returning Member Program’, which was facilitated from 2022 onwards for those who had won a major – or The Players Championship.
Five-time major winner Koepka was the only player to accept the offer and secured his return by paying a fine of approximately £63 million.
Amid reports that some LIV golfers have contacted the PGA Tour and DP World Tour to explore a possible return, it is unclear whether such a path would reopen following the possible end of the series, and what terms might be issued.
LIV Golf Virginia is scheduled to debut on May 7 at Trump National Golf Club just outside Washington, DC.
PIF has been contacted for comment.
Saudi Arabia hosts and invests in many sports, including football, boxing, Formula 1 and tennis.