"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," Saudi Arabia sports minister Prince Abdulaziz bin Turki Al Faisal told the BBC.
"It's the most-watched league in Saudi and the region and you have a lot of fans of the Premier League.
"We will definitely support it if any [Saudi] private sector comes in [to buy Liverpool or Manchester United], because we know that's going to reflect positively on sports within the kingdom.
"But if there's an investor willing to do so and the numbers add up, why not?" Prince Abdulaziz added.
Saudi investors already own a Premier League club after the takeover of Newcastle United last year.
Liverpool and Manchester United are up for sale with their American owner seeking to offload their stake in both clubs.