Southampton boss Mauricio Pellegrino has already held talks with the Spanish giants about signing Alcacer in January 2018.
But the 24-year-old former Valencia ace is not yet sold on a move to the south coast, prompting interest from French outfit Lille.
Pellegrino wants to improve his side’s efforts infront of the goal after leading Saints to just two wins in all competitions.
However, he is ready to listen to offers for the Spain international, who scored only six times last campaign.
Despite the predicaments at the Nou Camp, the Spaniard has a fine goal scoring record throughout his career, having been a prolific finisher during his teenage years at Valencia