The Armenia international, who joined the London club last week from Manchester United in a swap deal with Alexis Sanchez moving in the opposite direction, is likely to face Swansea on Tuesday.
Mkhitaryan struggled to pin down a regular starting spot at Old Trafford and was played in a variety of attacking roles during his 18 months at the club.
Mourinho has been criticised for an unwillingness to let his attacking players off the leash in big games despite the rich resources at his disposal.
"Of course it's very important to have respect from your manager," he told Arsenal Player. "I know that he's demanding and he likes his players to explore.
"He was one of the (reasons) to join Arsenal as well because everyone knows he's a great manager.
"I've known him for a long time and of course it was not very difficult to make this decision to come to Arsenal, because I think the way that Arsenal play (make) it a dream for every player to come here and play offensive football.
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