The Hammers are keen to add more bodies into their ranks before the start of the 2022/23 Premier League season.
Cornet, 25, is facing an uncertain future at Turf Moor following the Clarets’ relegation to the Championship.
David Moyes’ side are ‘monitoring’ his situation at the moment and haven’t made a move yet, with the Frenchman recently seeing a switch to top flight new boys Nottingham Forest stall, as detailed in a report by the Daily Mail.
The former Metz and Lyon man joined the Clarets in August 2021 on a five-year deal, and subsequently still has a decent amount of time left on his contract.
He made 26 league appearances last term and chipped in with nine goals.
Check out the latest Premier League transfer speculation below...
5. Werner available on loan
Chelsea are prepared to let Timo Werner leave on loan in the coming weeks, would be open to including an option to buy in any agreement. Newcastle United and Arsenal have both been linked. (Fabrizio Romano) | Getty Images
6. Rennes eye Kalimuendo
Leeds United target Arnaud Kalimuendo is a transfer priority for Rennes this summer. The French outfit are willing to pay up to £25m for the forward. (L’Equipe) | Getty Images
7. Spurs want Milenkovic
Tottenham are set to ramp up their interest in Fiorentina defender Nikola Milenkovic. (La Nazione) | Getty Images
8. Toon fail in Maddison bid
Leicester have rejected Newcastle’s £40m opening bid for playmaker James Maddison, are holding out for closer to £60m. (iNews) | Getty Images