Garcia was previously linked to a move to Arsenal last summer, but the transfer was blocked by Espanyol. He is also a target for Real Madrid, which adds to the competition for his signature.
Garcia's contract includes a buyout clause of £21m, which increases to £25m in the final weeks of the summer transfer window.
Manchester United are interested in signing Garcia, while Arsenal are still considering their options as they prepare to lose their on-loan goalkeeper, Neto, back to Bournemouth at the end of the season.