The Tigers are looking for a new first-choice keeper following their promotion to the top flight.
Steve Bruce used loan signings in goal for much of last season with the likes of Ben Amos and David Stockdale, but he now wants to bring in a permanent number one.
And Schmeichel appears his first choice, as Bruce has now returned for a second bid - but Leicester have already shunned that offer.
Bruce is expected to return again for the 26-year-old, who joined Leicester from Leeds in 2011.
The Dane enjoyed an excellent campaign and was named in the Championship Team of the Season.