Lukaku has missed United’s last two outings - victories at Bournemouth and Juventus - with a hamstring problem.
The Belgian has not started since the defeat to Juventus at Old Trafford last month, having been named as a substitute for the following weekend’s win over Everton.
Lukaku could, however, return in time for Sunday’s trip to the Etihad having recovered from his hamstring issue and started training again.
“Lukaku is training with the team this morning. If this answer is positive and we have of course one more session tomorrow, if the answer is positive he's ready [for City],” Mourinho said on Friday.
United will assess Lukaku after Friday and Saturday’s sessions before making a decision on his involvement at City.
“In this moment I can only say he trains with the team, I don't know his answer,” Mourinho added.
Lukaku lost his starting place last month following a goal drought which stands at nine games.
The 25-year-old’s last United goal came in the 2-1 win at Watford on 15 September.
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