Over the past week, it has been suggested that Ward was in contention to become the new number one at Anfield, with the Welshman in line to feature in a friendly against Blackburn Rovers on Thursday night.
However, according to The Sun, Leicester have offered £12m for the Wales international, a bid which has been accepted by the Merseyside giants.
Liverpool are on the brink of signing Alisson Becker from Roma for a fee in the region of £67m, and the Brazilian's arrival would take Jurgen Klopp's options between the sticks up to four with Loris Karius and Simon Mignolet also at the club.
Ward is now expected to hold discussions with the Foxes, who could entertain the possibility of selling Kasper Schmeichel later in the transfer window.
During the last campaign, Ward made just one appearance for Liverpool, which came against Leicester in the EFL Cup.