Nice president Gilbert Stellardo says Liverpool will jump to the head of the queue for Loic Remy if they match West Ham's offer.
The Hammers have matched Nice's €10million (£8.4m) asking price for the 23-year-old, but their instalment proposal is not to the club's liking.
Stellardo says the club are happy with the value of West Ham's offer, although Liverpool will be in pole position should they match their rival's bid.
Nice have no qualms cashing in on the France international, but insist they will require all the money up front and will not settle for an instalment plan.
Remy is one of France's hottest properties having scored 15 goals in 33 appearances last season and Tottenham are also rivalling Liverpool and West Ham for his services.
"For the moment it's the same status quo, but if Liverpool make an offer things will be done swiftly," he told L'Equipe.
"The amount (offered by West Ham) suits me but not the payment method.
"West Ham want to buy Loic because they think he could rapidly be worth €10million more if he plays in England. They don't want us to pay the full sum all at once."