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The Armenian has been linked with a move to the Emirates as a makeweight to bring Alexis Sanchez to United.
Arsene Wenger has accepted defeat in his efforts to keep the 29-year-old at the club and Sanchez is reportedly close to agreeing a deal worth £300,000-a-week at Old Trafford.
Mkhitaryan was not part of the squad this evening as United comfortably beat struggling Stoke 3-0.
And Mourinho refused to rule out the possibility of the former Borussia Dortmund joining the Gunners this month.
Henrikh Mkhitaryan next club odds
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“Arsenal is the only one I open the door for him to go and play, because I believe he is really a good talent, and he needs to play a part of that. ”
Man Utd boss Jose Mourinho
"He's a player that I like, of high quality,” he told Sky Sports.
“Is he going to be involved in one deal in leaving us? It's possible. But it's also possible that he stays.
"I'm just trying to protect him and the team, so let's make sure he stays with us or that he leaves us. The market is open.
"I have a squad of 22 players and I want to keep a squad of 22 players.
“Maybe just because I want to make the kid a good player, and I'm not giving him the chances that I'm giving to Scott McTominay, for example, because he plays in a position where I have so many players.
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"Arsenal is the only one I open the door for him to go and play, because I believe he is really a good talent, and he needs to play a part of that.
“The numbers we have, with the Premier League, Champions League, FA Cup, I have to keep the number of players we have."
United are now 12 points behind runaway leaders City.
They return to action on Saturday as they travel to Burnley (3pm).