Cornet impressed in his first Premier League season in Burnley colours but was unable to prevent his side from slipping down to the Championship.
The Clarets have already seen some of their starters from last season leave the club and Cornet is heavily with an exit with strong interest from the top flight.
Everton have already seen Burnley turn down their initial offer for the ex-Lyon star while it has emerged that Fulham have now entered the race to sign him.
But the forward could have yet more suitors in the top flight in addition to Everton and the Cottagers.
Nottingham Forest and West Ham are both keeping tabs on Cornet’s future at Turf Moor with the duo also in the market for attacking reinforcements.
Everton want to sign Cornet permanently while Fulham are seeking an initial loan deal for him.
And it remains to be seen whether the Tricky Tress or the Hammers act upon their interest and also join the race for the Burnley star this summer.
