Lukaku missed Belgium's 4-3 win over Bosnia at the weekend with a knock to his ankle and Mourinho will be hoping he does not aggravate the injury; particularly given teammate Marouane Fellaini will miss the clash with Liverpool having sustained ligament damage in the same game.
United visits fierce rival Liverpool on Saturday in what is likely to be its toughest match of the English Premier League so far.
Romelu Lukaku is in line to play for Belgium against Cyprus on Tuesday after coach Roberto Martinez insisted the Manchester United striker is fit.
"I have not had any communication with Jose Mourinho on the subject of Marouane", The Mirror quotes Martinez as saying. United have six games including playing Benfica in Lisbon in their third Champions League group match four days after facing Jürgen Klopp's team.
Each and every Monday during the season, Manchester United star Juan Mata pens a personal blog.
And Michael Carrick also drove in for training in his silver range rover, after picking up an injury himself.
Chris Smalling has played alongside some top talent during his time at Manchester United, and has now attempted to piece together a dream XI of Red Devils team-mates.
The England worldwide then opted for Patrice Evra at left-back, and Paul Scholes, Michael Carrick, Ryan Giggs and Paul Pogba in a midfield four, with Wayne Rooney and Marcus Rashford as his two strikers.