Mourinho called for the club’s World Cup participants to shorten their rest days after last month’s tournament to help United.
The club have also been hindered by injuries, and hope to avoid a poor start to the league season.
England duo Phil Jones and Marcus Rashford were already set to return early and United will now be boosted by Lukaku’s decision.
Man United prepare to host Leicester City in their first league game on Aug. 10.
“We will have (Victor) Lindelof who started training two days ago,” Mourinho said after United’s 2-1 win over Real Madrid in the pre-season International Champions Cup (ICC) on Wednesday.
“Marcus Rashford, Jones and Lukaku are coming back three days early to try to be available for the team.”
The Portuguese boss praised his senior players for the intensity they showed in United’s pre-season tour but insisted the fixtures did not reveal anything new strategically.
“I didn’t learn anything (tactically). I know what (Ander) Herrera is, I know what (Juan) Mata is, I know what (Alexis) Sanchez is, I know what they are…
“I know the kids need time to grow up,” Mourinho said.
“The boys tried everything, they gave everything, they know we have to try to fight for the best result but tactically it means nothing.”
United have won two of their five pre-season fixtures so far and will be keen to make a quick start in their quest to win silverware this season.
Mourinho was unsure, however, if Anthony Martial would return in time to play Sunday’s final friendly against Bayern Munich.
The Frenchman left the team’s pre-season tour early to attend the birth of his daughter.