Speaking to Portuguese media, Deco said: "Xavi submitted his resignation. He stays until the end of the season but no more.
"He revealed that he doesn't feel able to give the team the change it needs," Deco adds.
Xavi and his team suffered another disappointing draw to 19th-placed Granada at home.
Barca have now failed to beat Granada in the last five meetings between them with four draws and a defeat.
The implication is that Barca have slipped 10 points behind Real Madrid in the title race and are also five points behind Girona.