The Armenian has fallen out of favour under the Portuguese, having struggled to apply his game under the manager's approach, with United now willing to cash in in January and former club Borussia Dortmund emerging as his likeliest destination.
But Mourinho is set to give him a chance to impress at Ashton Gate on Wednesday evening with the midfielder having not started a game since November 5.
"It's possible he is involved," Mourinho said. "At the moment we are playing [Juan] Mata, [Marcus] Rashford, [Jesse] Lingard or [Anthony] Martial, [Romelu] Lukaku so on the bench being Ibra [Zlatan Ibrahimovic] and one of the other ones, Martial or Rashford and there is no space for everyone because you need balance on the bench, too."
With five games over the next 14 days Mourinho is set to shuffle his pack with the likes of Sergio Romero, Luke Shaw and Daley Blind all in line for much-needed game time.
But Mourinho will resist wholesale changes against one of the form teams in the second tier.
"I am making a few changes for the match, but not many because Bristol City is one of the best teams in the Championship and for me now the Championship is not the Championship of five or 10 years ago," he added.
"The Championship is now high quality teams with lots of players that could be playing in the Premier League easily. So we need to take the game really seriously, but I am going to make a few changes."
United are willing to let Mkhitaryan go at the right price, and Dortmund have so far shown the strongest interest. That stance would be in line with the Bundesliga club's previous policy as they have regularly shown a willingness to bring back former players who have struggle elsewhere, such as Mario Goetze, Nuri Sahin and former United player Shinji Kagawa.
Such a deal might also suit Old Trafford's plans for incoming players, as Mourinho does want a defensive midfielder, and Dortmund's Julian Weigl has long been a target. While any kind of direct swap is unlikely, a move could facilitate negotiations.
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