The Armenian had been in brilliant form, scoring two goals and registering five assists in the first few weeks of the season, but has found himself out of the team since United lost 1-0 away to Chelsea in November.
Henrikh Mkhitaryan is among those struggling to get into Mourinho's team after failing to even make the bench in seven of the last eight games.
"I think for the right price", said Mourinho, when asked if he would listen to offers in such circumstances.
Fair enough you might think, but it is common for players to go the easier route and simply vote for their club manager in this sort of thing.
"I don't speak about players, especially players that belong to other clubs - there is no sense", he said.
Mourinho also confirmed there were no fresh injury concerns for his side following their gritty 1-0 win over Bournemouth in mid-week and he would use the same squad for Sunday's trip to the Baggies.
Explosion in Christian Church in Pakistan: 5 Reportedly Killed, 16 Injured
On the instructions of CM Balochistan and Health Ministry, an emergency has been declared in public hospitals of Quetta . One terrorist was shot down at the gate by police while the other ran inside and blew himself.
The Belgium global has scored two goals in his last three games following a run of one in 12 but refused to celebrate after finding the net in the 1-0 win over Bournemouth on Wednesday.
If City were to drop points against the resurgent Lilywhites, United could trim the gap at the Premier League summit by beating West Brom the next day.
It has always been fashionable to compare and contrast Mourinho and Pep Guardiola's brands of football, but it is not unreasonable to wonder if Mkhitaryan's skill-set, turn of speed and technique would be better suited to Manchester City's attacking system than United's more rigid set-up.
"If you score a goal in the last minute that gives you the victory in the last minute then yes. you lose your balance and you don't control your emotion: you react in an emotional way".
"I'm not acting to the cameras or the fans".
"I didn't celebrate either", said Mourinho.