The Filbert Street outfit are keen to sign the £800,000 star, who has been the subject of a number bids from interested clubs during the pre-season.
The former York City forward turned down moves to Bristol City and Preston North End after the club's had agreed a fee for the player's signature.
Cresswell has been in and out of Paul Jewell's side this season and he has been unsettled at Hillsborough, as he feels he hasn't been given a fair chance at the club.
Leicester boss Peter Taylor has targeted Cresswell as an important signing, having worked with him previously in the England under-21 set up.
A move back into the Premiership would appeal to Cresswell and he is expected to sign on at Filbert Street in the next few days.
If Cresswell does join it is sure to raise doubts over Tony Cottee's future at the Midlands club as speculation continues to link the former West Ham striker with a move back to London
