The owners of both Premier League clubs are exploring potential sales.
Newcastle United already has Saudi Arabian owners after a takeover backed by the Saudi Public Investment Fund was completed in October 2021.
Prince Abdulaziz bin Turki Al Faisal said there was a lot of “interest and appetite” in United and Liverpool.
He told BBC Sport: “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.
“It’s the most-watched league in Saudi and the region and you have a lot of fans of the Premier League.