Lukaku picked up an ankle injury during last weekend's 2-1 win over Arsenal in the Premier League, and it had initially been feared that the Belgium international could miss the remainder of the season.
Mourinho has admitted that he 'does not know' how long the 24-year-old will be out of action, but he will play no part against Brighton on Friday night.
"I don't know, I just know that of course not tomorrow, apart from that we need to wait for more scans, more time," Mourinho told reporters at Thursday's pre-match press conference.
However, the Portuguese revealed that it "looks positive" when quizzed on whether the striker would be fit for the FA Cup final against Chelsea on May 19.
Lukaku has scored 27 times in 50 appearances for United this season.