The Armenian argued with Mourinho after watching a video of United's 1-0 win over Brighton & Hove Albion from November 25.
Mkhitaryan has not featured for the Red Devils since that win over Brighton and has been left out of the squad for seven of the club's last eight games, per football writer Liam Canning:
Liam Canning @LiamPaulCanning
Luke Shaw's done well to slowly convince José Mourinho to start him and be involved more. Now Henrikh Mkhitaryan has a big test of character. Has been left out of the squad in seven of the last eight matches. Not good.2017-12-13 19:16:25
Mourinho's decision to keep overlooking the 28-year-old suggests his future at Old Trafford looks really bleak, per football writer Hesham Bilal-Hafiz:
Hesham Bilal-Hafiz @hesham786
No Mkhitaryan in the squad again. Genuinely looks like he could even leave in January at this rate, if he can’t get a game in a CL dead rubber or in a midweek game v Bournemouth, it’s looking very bleak. #mufc2017-12-13 17:55:13
Per Custis, the United boss has said that unhappy players can leave the club: "Every player has a price. If a player is not happy, brings with him the request with the number that we consider good for us, I'd never say no."
Mkhitaryan started the season brightly with five assists in just his first three Premier League games but, after a series of disappointing displays, has been gradually frozen out:
B/R Football @brfootball
Henrikh Mkhitaryan is getting frozen out at Manchester United ❄️ https://t.co/JN5W73dXiY2017-12-14 22:12:59
There's no denying the former Borussia Dortmund man's talent, but he has been unable to produce his very best on a consistent basis for United.
He has clearly lost Mourinho's trust and it's really difficult to see a way back for him at United at present, meaning a January transfer might be the best solution for both player and club.
Fellaini could also be on his way out of the club this winter. The Belgian is out of contract next summer and has been unable to agree a new deal, per the Telegraph's Ian Whittell.
Mourinho allowed the unsettled duo of Memphis Depay and Morgan Schneiderlin to leave last January and "will adopt a similar stance in this window."
Fellaini may not be an automatic starter under Mourinho but has proved to be a useful squad member with four goals in 11 Premier League and UEFA Champions League appearances.
The Belgian's strength, aerial ability and eye for goal mean he brings a different dimension to the United team, particularly off the bench.
The 30-year-old has held talks with Besiktas but may struggle to get a deal done as Mourinho wants to keep him, per Emre Sarigul at Turkish Football:
Turkish Football @Turkish_Futbol1
LATEST: Fellaini's representatives have held several rounds of talks with Beşiktaş & Galatasaray. Four-year deal, €4-5m per-season are the numbers were talking. Would have been a done deal but #MUFC boss Mourinho is throwing a spanner in the works. Does NOT want to lose him2017-12-13 14:03:06
However, if Fellaini is unable to agree a new deal, the club may opt to sell him this winter, rather than see him walk away for free when his contract expires in the summer.