The Ivorian was a source of inspiration as the club valiantly battled against relegation last term, but it appears that his spell with the Clarets will come to an end after just one season.
It was an impressive coup to bring him to Turf Moor, after Cornet had been a key cog for Lyon in Ligue 1 and the Champions League in the last few seasons.
With four years left on his deal at the club, Burnley are set to pocket a hefty fee if he does depart.
Vincent Kompany had his say on the situation when he spoke to the Burnley Express.
He said: “I don’t know close it is.
“It is no secret there is a couple of clubs in for him, and a couple of clubs have made good offers.
“We have to prepare probably for a period after him, and that is what we are doing.
“I am not saying Maxwel has gone, he has offers.”
With Wout Weghorst and Cornet potentially departing this summer, it is going to be interesting to see who leads the line ahead of Scott Twine at Turf Moor this season.
Quiz: The big Burnley summer quiz – Can you score 30/30 without using Google?
Twine was prolific in providing goals and assists for Milton Keynes Dons in League One last season, but it would be a huge ask for him to be their main goal threat in aiming to return to the Premier League at the first time of asking.
Jay Rodriguez, Matej Vydra, if he signs a new deal, and Ashley Barnes have all succeeded at the level previously in their careers, but not recently enough to feel like a safe bet to score 15-20 goals.
Having played such a well-established brand of football for so many years under Sean Dyche, it is going to be interesting to see how long it takes Kompany to get his ideas across and have the Clarets playing the way he wants them to.