The Mexican frontman has found first-team opportunities limited at Old Trafford this season, following the arrival of last year's Premier League top scorer Robin Van Persie.
Hernandez started alongside Van Persie and Wayne Rooney in United's most recent Champions League tie against Cluj, but the diminutive forward has started just two of Manchester United's last 11 Premier League matches.
Hernandez has found himself well down the pecking order at Old Trafford, with Van Persie, Rooney and Danny Welbeck all thought to be ahead of the Mexican striker.
Welbeck's versatility edges him in front of Hernandez, who can only really operate through the middle, whereas the England international can play out wide if necessary.
Jose Mourinho has Gonzalo Higuain and Karim Benzema as forward options, and is thought to be interested in bringing in Hernandez as a third rotation.
The United striker signed a five-year deal last year, but after a sensational debut season at Old Trafford, Hernandez failed to hit the heights last year.