The Mirror says West Ham boss Avram Grant is poised to beat Liverpool to the signing of Remy.
Despite Liverpool's interest, West Ham appear in the box seat to sign the player after Nice sporting director Patrick Governatori said the Ligue 1 club is prepared to accept an improved £11.3million bid from the Upton Park outfit.
Governatori said: "On Tuesday we received a new proposal from West Ham, for a full payment in cash.
"If Liverpool want to sign Loic, we need clear rules and commitments from them. But West Ham are hot for the player and we want to complete the transfer before the end of the month."
Remy is now expected to join the Hammers after a farewell appearance for Nice in this evening's friendly with Grenoble.