The England under-21 international started his first Premier League match this campaign under Puel in last Saturday's 2-0 win over Everton, where he created the first goal and scored the second.
"We obviously wanted to see who the new manager was...but I'm happy playing football here and let my representatives deal with that side of it. When they give me the phone call we'll get it sorted," Gray told British media.
"It's for my representative and the backroom staff to deal with. All I can do is what I've done (against Everton) and when it comes to getting sorted out we'll get to it."
Gray, who joined from Birmingham City in January 2016, had previously bemoaned his lack of playing time under Leicester's former managers, Shakespeare and Claudio Ranieri, as 21 of his 30 league appearances last season were as a substitute.
Leicester will be keen to extend their two-match winning streak in the league when they travel to Stoke City on Saturday.
(Reporting by Aditi Prakash in Bengaluru; editing by Amlan Chakraborty)
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