Lukaku was injured in a tackle with Arsenal defender Konstantinos Mavropanos in United’s 2-1 victory over the Gunners on Sunday.
The Belgian striker had to leave the field with Marcus Rashford replacing him.
United confirmed after that they face ‘an anxious wait’ to find out the severity of Lukaku’s injury with his availability for next month’s FA Cup final now in doubt.
Manchester United face Chelsea at Wembley on May 19 and Mourinho is unsure whether his No 9 will be fit.
“I don’t think it’s something, or I hope it’s not, that in this moment keeps him immediately out of a game that is in three weeks’ time,” Mourinho said.
“But I don’t know. I never, when I finish a game and a player is injured, immediately go for good or bad news. I wait a bit more.
“I don’t know if he is going to be out, or if he’s not okay. He wants to play all the time. He is never tired and, when he has small things, he doesn’t care. He still wants to go.
“So, for him to say immediately, to change him, it is because he couldn’t play. But there are three more weeks until the final, so let’s see. I know it was on his foot but I don’t know more yet.”
Manchester United face Chelsea in the FA Cup final having beaten Tottenham 2-1 in the semi-final.
Chelsea were 2-0 winners over Southampton with Olivier Giroud and Alvaro Morata goals proving the difference.
The FA Cup is the last chance for either team to lift silverware this season.