The Sun says the 23-year-old has attracted interest from around Europe after scoring 15 goals in 23 games in Ligue 1 this season.
But Lorient president Loic Fery insists he will do everything in his power to keep Gameiro, despite his contract expiring in June next year.
He said: "We can imagine three possibilities. Let him go at the end of his contract, transfer him this summer or extend his deal at Lorient.
"We've made considerable efforts — so far unsuccessfully — to try to extend his contract. I have not given up. Nothing is ruled out."