Tigers boss Steve Bruce has made a new No.1 one of his top priorities this summer and Schmeichel is thought to figure highly on his wanted list.
Hull had loan signing David Stockdale as their No.1 keeper this season and they were hoping to make his move permanent, but so far they have been unable to agree a deal with Fulham for the keeper.
It means Bruce has now stepped up his interest in Schmeichel as he looks to reshape his squad as he plans for life back in the Premier League.
Schmeichel enjoyed another fine season at Leicester and helped them reach the play-off semi-finals only to lose to Watford.
The Denmark international is entering the final year of his contract at Leicester and Hull hope the lure of the Premier League will boost their chances of landing the 26-year-old
Leicester are loath to lose Schmeichel, but are bracing themselves for bids for the former Manchester City youngster.