Sky Sports understands Leicester are weighing up a move for Fitz Hall on a free transfer.
The former Crystal Palace and Wigan man is available after recently being released by Queens Park Rangers.
Hall found first-team chances hard to come by last season and Hoops boss Mark Hughes decided to let him move on.
The news has alerted a host of clubs, but Leicester are hoping to win the race for the 31-year-old.
Leicester boss Nigel Pearson is thought to be an admirer of Hall and sees him as a key addition to his squad for next season.