The Armenia international completed a move to Arsenal in a swap deal from Manchester United in the January transfer window.
Mkhitaryan moved to the Gunners as Alexis Sanchez finally left Arsenal following months of speculation to move to Manchester United.
The Gunners star made three assists on his home debut to help Arsenal ease to a 5-1 win over Everton at The Emirates last month.
Arsenal have lost four of their last five games in all competitions with Mkhitaryan unable to restore some positivity at the north London side.
The former Dortmund playmaker was quiet throughout Arsenal’s 3-0 loss to Manchester City in the Premier League on Thursday night.
Mkhitaryan won a second-half penalty which was missed to deny the Armenian midfielder an assist.
Former Arsenal defender Keown believes Mourinho will be delighted to offload Mkhitaryan following his underwhelming performances over the past month.
“We’ve talked about Ozil not doing a great deal but I’m sure Mourinho will be thinking he’s done a good deal out of Mkhitaryan because I’m sure we’d have seen more from Sanchez,” Keown told BBC Radio 5 Live.
“We’ve just not seen that fire from Mkhitaryan. He’s been quiet. He’s played in a wide position but I think he’d be best served more central.”
Arsenal finished in fifth place in the Premier League last term to miss out on a spot in the Champions League.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news