The England U21 international is believed to be keen on more regular game time ahead of the coming season and has been linked with moves to the likes of Tottenham and Everton.
The former Birmingham City man made 41 appearances in all competitions for the 'Foxes' last season but he started just nine Premier League games.
Speaking after Leicester's friendly with Burton, manager Craig Shakespeare admitted that he had spoken to Gray about giving him more minutes on the pitch this season.
"We've had conversations, myself and Dimi. It is well-documented. We have spoken about trying to give him more game-time and we are both happy with that," he explained.
Shakespeare will be reluctant to lose another winger, with Riyad Mahrez keen to leave the lcub this summer after attracting interest from the likes of Arsenal and Roma.