The 24-year-old, who has scored 16 league goals and provided seven assists in 34 appearances for United, was substituted in the second half of last weekend's 2-1 victory over Arsenal.
Lukaku posted pictures of himself recovering at the Move to Cure Clinic in Belgium on his Instagram account earlier on Thursday.
"I just know that, of course, (he is) not (available) tomorrow. Apart from that, we need to wait for more scans, more time but not tomorrow," Mourinho told a news conference.
"Hope so. Looks positive," the Portuguese added when asked about Lukaku's hopes of playing in the FA Cup final against Chelsea on May 19.Lukaku's compatriot Marouane Fellaini was quoted by British media saying that United made a mistake in not extending his contract last year and that he was willing to move away from the club when his current deal expires in June.
Mourinho believes that contract talks between United and Fellaini have been positive but says the final decision on a new deal rests with the midfielder.
"Still positive. He's important, he's a player I like. But if for him he has a different position in relation to other players with contracts - we can control their destiny in a different way," the Portuguese boss added.
"The destiny is in his hands, he'll decide what makes him happy. He knows I want him to stay, the club do, he has an offer but it's up to him now."
Defender Eric Bailly has missed United's last three league games and Mourinho says the Ivorian's absence is due to his nation's failure to qualify for the World Cup finals in June and July.
"He's the only central defender whose country is not in the World Cup so if I have to make a kind of more emotional effective choice to help my players he's the one I'm not going to help," Mourinho added.
"When I look to the other four central defenders fighting for a position in the World Cup I am giving less to Eric."
After the trip to 14th-placed Brighton, second-placed United travel to West Ham United before ending their league campaign at home to Watford.
Sumber Lukaku out of Brighton clash, says Mourinho