Schmeichel has been in excellent form for the Championship toppers this term, but he could be set for a summer exit with his contract due to expire at the end of the season.
The Foxes are thought to be keen to keep their man, yet the Dane is reluctant to commit himself just yet.
United have been credited with an interest in the glovesman on a number of occasions, but it is thought that their desire to land him has spiked recently as David Moyes plots to bring in backup for David de Gea.
The player’s agent, Mads Frederiksen, confirmed that interest from big clubs is high:
“Kasper has played on a very high level for a long time, and we can also notice a lot of interest from many clubs. His performance against England doesn’t make the interest smaller.
“From a commercial perspective, it opens up some great opportunities for Kasper in relation to personal sponsorships, so it’s a very exciting time for him.”