The 27-year-old has made only two starts for the Hammers since joining them from Burnley back in the summer of 2022.
Cornet's only league appearance this season came as an 89th-minute substitute in the 1-1 draw against Bournemouth in August.
According to talkSPORT, West Ham are now prepared to part ways with the Ivorian winger, who has never managed to solidify a regular starting spot under manager David Moyes.
The report adds that Cornet has fallen a long way down the pecking order at West Ham, and the club are prepared to listen to offers for him in the upcoming window.
The 26-year-old recently recovered from a serious calf injury that kept him sidelined for a little over four months.
Cornet has made 27 appearances in total for West Ham in all competitions since his £17.5m move from Turf Moor.
The Hammers are back in Premier League action on Sunday when they head to Craven Cottage to take on Fulham.