Gray, 21, was largely used as an impact sub last season, starting just nine games for the Foxes during an often frustrating campaign for the former Birmingham City youngster. Bournemouth and Crystal Palace were both heavily linked with a move for the winger during the summer transfer window, while Tottenham were said to be the front-runners heading into the final day of the transfer window.
Gray recently confirmed there were offers for his services on deadline day, but appeared open to remaining at the King Power Stadium, with Craig Shakespeare adamant the England Under-21 international has a "big future" at the club.
And speaking ahead of Leicester's trip to Huddersfield Town, the Leicester boss insisted a new deal for the player is nearing completion.
"I am aware that it is close. It has been ongoing for a while," Shakespeare said. "The sooner that it is put to bed the better for Demarai. We spoke before about him being an integral part of what we are about and hopefully we can put that contract to bed."
The Daily Telegraph understands Gray will sign a new deal worth £50,000 a week before the end of September.
Leicester, meanwhile, are hoping to receive an update on the Adrien Silva transfer saga within the next two days. The 2015-16 champions struck a deadline day deal with Sporting CP but missed their deadline to register their new player by 14 seconds.
Leicester have launched an appeal against Fifa's decision to block the move, with Shakespeare hopeful of a breakthrough soon.
"Unfortunately it is still an ongoing process," Shakespeare said. "I would love to be in a position to say he is available for selection. But as a football department we are just waiting for the legal processes to take care of things. I don't have any hold on that. I am waiting for news. I am waiting for an update, which hopefully I've got in the next 24 or 48 hours."