The Daily Express newspaper in the UK reports that the 27-year-old is set to sign on for more at Welford Road, where he has forged a successful partnership with England and Lions captain Martin Johnson in the Welford Road engine-room.
The big forward should put pen to paper sometime in the next fortnight, before he takes on France in a crucial Six Nations Championship game.
Kay told the paper: "I'm happy here. Leicester is a club with a nice atmosphere and the best and most fans in the country. There is a good buzz about the place for the run-in."
Since making his debut on England's North American tour in 2001 – while the Lions were in Australia – Kay has been a key figure in the England second-row, battling with Bath's Danny Grewcock for a starting place recently and has won 14 caps to date.
His apparent intention to sign on for more with Leicester comes amid reports in France that Biarritz's veteran lock Olivier Roumat could be set to cross the English Channel and join the Tigers, although on a short-term deal mainly intended to cover for Kay and Johnson's absence during the Rugby World Cup.
Kay is in action this weekend for his club as the Tigers take on old rivals Bath away from home in the Zurich Premiership, looking to capitalise on their recent Cup form to help secure a place in the end of season play-offs.
By Mark Smith