The 24-year-old's existing deal at the King Power Stadium is due to expire next summer, and it does not appear that the former England Under-21 international will be penning a new contract with the Foxes.
Gray has been restricted to just one first-team appearance for Brendan Rodgers's side this season and has not even been involved in the squad for a Premier League match in 2020-21.
Journalist Duncan Castles has claimed that "there is an interest from Tottenham" in a player who has featured on 132 occasions in the Premier League.
"Here you've got a player available at no transfer fee cost who can help sort out that problem," Castles said on the Transfer Window Podcast. "I'm told that at Leicester they believe that he will be moving to Tottenham Hotspur.
"My understanding is that there is an interest from Tottenham, but that is not a guaranteed deal, he has interest from other Premier League clubs, there is also significant interest from overseas.
"A decision will be made as to where the best opportunity to develop his career is going forward once he's in a position to properly talk to the clubs."
Gray has scored 13 times and registered 17 assists in 168 outings for Leicester in all competitions.