Schlupp has been on trial with United since January, and has featured in the last two under-21 matches for the Premier League leaders.
The Old Trafford coaching staff have been impressed by the Leicester youngster's ability, and United have seen enough to persuade them to offer £1.5m for the 20-year-old.
The potential deal could rise to £2.5m depending on performance related add-ons.
And Leicester manager Nigel Pearson appears resigned to losing Schlupp. He 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."
Schlupp has played at left-back and up-front for the Foxes this term, and began his trial with United two months ago after impressing Old Trafford scouts in the Championship.
Leicester retain the ability to recall the Dutchman at any time, and he could return to feature against Leeds United on Tuesday night, according to the report.
If a deal with Leicester is concluded, the agreement would mean Schlupp is ineligible to play until next season - and he'd likely remain in the Championship with Pearson's side until the summer.
Leicester have a good relationship with United - Old Trafford youngster Michael Keane is currently on loan at the King Power Stadium and Danny Drinkwater and Ritchie De Laet - two former-United academy players - both now play for the Foxes.