The ownership of both clubs could change hands with Manchester United saying they're 'exploring strategic alternatives', while Liverpool have said they're welcoming new investors.
Liverpool, who have won more major honours than any team in England, and Man United have been linked with possible investments from the Middle East.
Saudi's sports minister, Prince Abdulaziz bin Turki Al-Faisal, would back any bids from the private sector, he has revealed.
"It's the most-watched league in Saudi and the region and you have a lot of fans of the Premier League," he told the BBC.
"From the private sector, I can't speak on their behalf, but there is a lot of interest and appetite and there's a lot of passion about football.
"We will definitely support it if any [Saudi] private sector comes in, because we know that's going to reflect positively on sports within the kingdom."
The kingdom's state-backed Public Investment Fund (PIF) have already bought Newcastle.
Despite ruling out an official bid from the Saudi government, the prince did leave a door open for private companies in the oil-rich nation to get involved.
He added: "If there's an investor willing to do so and the numbers add up, why not?"
Prince Abdulaziz also revealed he would love to see Ronaldo play in the Saudi league, along with the Saudi Arabian Football Federation.
The 37-year-old revealed in his interview with Piers Morgan that he was the subject of an offer from an unnamed Saudi club in the summer.
"Anything is possible, I would love to see Ronaldo play in the Saudi league," Prince Abdulaziz said.
"It would benefit the league, the sports eco-system in Saudi and it will inspire the youth for the future. He's a role model to a lot of kids and has a big fan base."