The Manchester Evening News report that the Ecuador international is fighting for a place in the United team next season.
The 31-year-old winger did put on an impressive performance in the 5-2 victory over Galatasaray last Saturday setting up Zlaten Ibrahimovic with his first goal for the club.
Valencia is into the final year of his contract and the Lions would be able to sign him as a free agent next summer but are keen on strengthening their attacking options over the current transfer window.
The Lions are also targeting a loan move for Bastian Schweinsteiger who is set for an exit this summer after being relegated to training with the reserve side.
Galatasaray have been banned from European competition this season due to breaching FFP rules. The Lions had a disappointing league campaign but did end up winning the Turkish Cup.