The Ghana international, who scored a hat-trick on his full debut for the Foxes back in August 2011, has been training with Sir Alex Ferguson's men for over a month.
During this time, he has impressed in two under-21 games against West Ham United and Liverpool.
Schlupp had shown promise when, upon his return from a loan spell at Brentford, he was given his first taste of Championship action under Sven Goran Eriksson back in 2011.
However, he has since dropped down the pecking order under Nigel Pearson and has been resticted to few first-team appearances.
National reports claim the Red Devils are set to make an offer of around £2 million for the youngster.