Alan Nixon of The Sun (h/t Metro) reported the right-back can negotiate a free transfer away if the United board do not activate an extra year option in his current contract. Valencia would be able to sign a pre-contract agreement in March, paving the way for his exit.
Per Metro, Mourinho has reportedly accused the Ecuador international of being overweight and dropped him from the starting XI after the player "liked" an Instagram post heavily criticising The Special One at Old Trafford.
Valencia has been one of Mourinho's favoured lieutenants during his two-year tenure in Manchester, but the converted winger has failed to sparkle at full-back.
At 33, the player is now past his best, and the recent arrival of Diogo Dalot from Porto has excited United supporters.
Valencia immediately apologised for his misdemeanour when it came to light he had "liked" an Instagram post calling for Mourinho's removal:
Antonio Valencia @anto_v25
Yesterday, I liked a post on Instagram without reading the text that accompanied the picture. These are not my views and I apologise for this. I am fully supportive of the manager and my teammates. We are all giving our everything to improve the results. https://t.co/bMEsrAwMkh
The incident saw Valencia dropped for the last Premier League match against Newcastle United at Old Trafford, as the hosts overturned a two-goal deficit to win 3-2.
Ashley Young took Valencia's place on the day, and both Dalot and the England international give Mourinho immediate options if the Ecuadorian leaves.
The reported problems between player and manager add more weight to the building issues playing out at the Theatre of Dreams.
Per the Daily Mail's Chris Wheeler, Pogba is "desperate to leave" as Mourinho loses his grip in the Old Trafford dressing room. The club has multiple players coming to the end of their current deals, and the disharmony between manager and squad is a huge cause for concern.
Wheeler added Luke Shaw is also out of contact at the end of the season, and he intends to let his deal run out if Mourinho remains in charge.
Valencia would not be a huge loss for United, but considering he is one of Mourinho's trusted players, it shows the tone and shade at Carrington is a depressing one.
Mourinho needs results fast. Only victories can save his job if he is to stay as manager until the end of the campaign.
United will want to retain their biggest stars who require new deals, and the coach could pay the ultimate price for the consistent conflict he creates with his top talents.