The 29-year-old spent the second half of last season on loan at Sevilla after making just 11 Premier League appearances for the Swans.
According to Sevilla ABC, Newcastle and Fulham have made late attempts to bring the Spanish player back to the Premier League, despite a likely permanent move to Sevilla already being in place.
Despite interest from England, the player's representative Luis Alonso has insisted that Mesa wants to stay in Spain.
"There is someone in the Premier [League] who knows him well," admitted Alonso.
"There are European coaches, from Serbia, who know what they can give. Roque only wants to hear about Sevilla. Already decided. We are waiting for everything to close, but we will have to wait until it is signed.
"Sevilla has also told us that he wants us to stay and we are here. When two love each other there are no problems."
Cottagers boss Slavisa Jokanovic has the same agent as the Championship player.