The Ecuadorian winger is one of several first-team stars expected to leave Old Trafford at the end of the season. Anderson, Nani, Anders Lindegaard and Javier Hernandez are all also under threat as United look to cut costs.
The report claims United will feel the pinch after Sir Alex Ferguson's insistence on beating Manchester City to the signing of Robin Van Persie.
The former-Arsenal striker cost the club £24m and his £250,000-a-week salary has stretched the wage budget to the limit.
And the January capture of Wilfried Zaha, for a fee in the region of £17m, put further pressure on the United coffers. It was reportedly brought forward after it became clear that United would face strong competition from their Premier League rivals for the England under-21 star.
Ferguson had attached considerable importance to the signing of Zaha, but the winter move has put a serious dent in the club's summer budget.
A Manchester United source told Goal.com: "Sir Alex and the club made it abundantly clear they would go that extra yard for Robin. United knew the numbers involved but saw it as a real sign of intent going forward.
"A couple of other targets had to slide as a result, certainly Lucas Moura, when Paris St Germain made their interest known in the boy.
"Those figures were just crazy. Wilfried Zaha is a sound investment due to the relatively low money involved. Sir Alex knows he will have to be even cuter this summer as a result of Robin now being on our wage bill."
Any transfer activity at the end of the season then will likely have to be partly financed by outgoings. Anderson, who's struggled with injury throughout his time at Old Trafford, has been linked with a number of South American clubs, while Lindegaard has failed to dislodge David De Gea as United number one.
Hernandez is highly-rated by Ferguson, but with Van Persie, Wayne Rooney and Danny Welbeck, the Old Trafford boss has plenty of options going forward.
That could make Hernandez available for the right price, with Atletico Madrid thought to be keen to sign the Mexican as a potential replacement for the in-demand Radamel Falcao.
Valencia and Nani have both won United Players' Player of the Year awards in recent seasons, but neither has managed to find their best form this term.
Valencia looks a shadow of the player he was last season, with injury partly to blame for his loss of form. The Ecuadorian international was a first-team regular during the last campaign, but has looked out-of-sorts recently.