The winger has grown impatient at his lack of game time and his manager Brendan Rodgers is reportedly growing resigned to losing him. Gray has been limited to coming off the bench as he competes with an array of attacking talent at the King Power.
The Athletic reports that the 24-year-old is attracting interest from several clubs, not least Spurs.
But no concrete offers have yet been submitted for the ex-Birmingham City ace.
Tottenham's high-profile signing of Gareth Bale would be a further stumbling block to first team football if Gray was to move to North London this season.