Rashford declared this week he was "ready for a new challenge" in an indication he's planning to leave in January.
TalkSPORT says Al Ahli, Al Ittihad and Al Qadsiah are all interested in the England international for next month's market.
The Saudi interest would centre on an initial loan arrangement. For now, United are yet to field any formal approaches for Rashford.
“I’m halfway through my career. I don’t expect my peak to be now," said the forward.
"I've had nine years so far in the Premier League and that’s taught me a lot, that’s helped me grow as a player and as a person.
"So I don't have any regrets from the last nine years.
"I won’t have any regrets going forward because I take things day by day and sometimes bad things happen, sometimes good things happen. I just try and keep a fine balance."