Cornet faces a season in the Championship with Burnley, but his stock is still high in the Premier League and he has been linked with a host of top flight sides, including Everton.
West Ham are trying to improve in their attacking department and are also looking to sign the winger, on a permanent basis.
So far, they have not yet reached agreement with Burnley but the Hammers are persistent and are not giving up.
West Ham are working hard to win the race for Cornet’s signature as they look to sign a player who operates on the left side of the field.
The Hammers have been looking to sign Filip Kostic from Eintracht Frankfurt, but that swoop now looks to have fallen through.
West Ham are keen to beat Everton and Newcastle in the chase for Cornet and are making concentrated efforts towards that purpose.
Cornet was the leading goalscorer for Burnley last term, with nine goals, and he is suggested to be eager to return to the Premier League.