The 20 year old has been on trial at Old Trafford for over a month and featured in two under-21 games against Liverpool and West Ham last week.
The Ghana international is mainly known as a striker, but has also played as a left-back for the Championship club this season.
"We'll be discussing this week what the next step is," boss Nigel Pearson said.
"As soon as we find that out we will let you know. He has done well."
Former Leicester manager Sven-Goran Eriksson, who gave Schlupp his debut, told BBC Radio Leicester: "He's a very, very good football player with very good talent. I wanted to keep him.
"If he is ready for Manchester United, I do not know. It is a big thing for him but would be a big loss for Leicester if it happens."