The Telegraph reports that United are in pole position to sign Schlupp in a £1.5million deal.
The Ghana international has featured in the last two under-21s games for United.
The 20-year-old was invited for a trial at Old Trafford in January.
Leicester manager Nigel Pearson said: “I think we’ll be discussing this week what the next step is. 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.”