Belgium international Lukaku is understood to be staying behind after training sessions have finished up at Carrington to work with the England starlet.
Manchester United boss Jose Mourinho launched an impassioned defence last week against accusations he is hampering Rashford's progression due to a lack of starting opportunities, citing no player under the age of 21 has played more competitive minutes for a Premier League team than the academy graduate since his debut in February 2016.
And the young striker is also receiving plenty of extra tutelage away from prying eyes, with Lukaku helping Rashford on some of his finishing and movement on the training ground.
Mourinho is believed to still hold reservations that the Manchester-born youngster will go on to become a main striker, although Rashford will certainly be earning brownie points from his manager by putting in extra time honing his eye for goal.
Lukaku is also impressing Mourinho with his commitment to the squad cause, becoming an ever-growing influence inside the dressing room since his £75m switch from Everton last year.