Valencia is out of contract at the end of the season and has struggled for form and fitness in recent months.
According to The Sun, Newcastle and Fulham are sniffing around.
With his contract running down, the Red Devils will let him leave for free or on loan.
Newcastle boss Rafa Benitez wants to add experience to his back line.
It’s suggested he’ll make a move if United cancel Valencia’s contract.
Fulham have upped their interest after Claudio Ranieri missed out on his top target.
The Italian chief wanted Victor Moses but he’s opted to join Istanbul-based heavyweights Fenerbahce from Chelsea.
United are in stunning form under Ole Gunnar Solskjaer.
The Norwegian has now masterminded eight victories on the bounce.
The Red Devils eased past Arsenal with a 3-1 win on Friday night.
“I thought there was a gulf between the two teams,” ex-United defender Phil Neville told the BBC.
“At the start people accused Ole of winning easy games, then he went to Tottenham and won [two weeks ago].
“The players that were not performing under Jose are now performing the way we knew they could.
“It was a brilliant performance from United.
“I think what we have seen from Ole is that it’s more than just giving people love, it is about tactical awareness.”
Match of the Day host Gary Lineker echoed Neville’s observations.
“They look happy, they look like they’re enjoying their football,” he said.
“It’s the antithesis of what they were at the start of the season.
“What Solskjaer has done is remarkable.
”It’s probably the greatest audition in the history of football in many ways.”