Mkhitaryan started the 2017-18 campaign in impressive fashion, but the Armenian has failed to make the United squad in seven of their last eight matches.
The 28-year-old has been linked with a return to former club Borussia Dortmund amid suggestions that Mourinho would be prepared to sell for the right price next month.
According to Smith, Mourinho could look to use Mkhitaryan to potentially sign a new player in January, although the 55-year-old has said that the attacker may well still have a future at Old Trafford.
"Who knows what will happen in January? There will be plenty of offers for someone like Mkhitaryan," Smith told Sky Sports News. "Whether they will be the right place or not is another matter.
"He is a sellable asset and a bargaining chip perhaps for somebody else that Mourinho might want to get in. I still think he would be reluctant to sell somebody like that, who is a quality player when he is playing with confidence."
Mkhitaryan was reportedly involved in a training-ground row with Mourinho last month after taking exception to comments from his manager.