The German-born Ghana international has been training with United since January.
The 20-year-old is understood to have impressed and talks are continuing over his future, as he has featured in recent games for United's Under-21 side.
Leicester could still recall Schlupp and use him, and manager Nigel Pearson says they will talk with United.
"I think we'll be discussing this week what the next step is," said Pearson.
"He's done well at United, he's played the last two games that he can play there so clearly it's going to have some effect this week."