The two clubs remain apart in their valuations with the Gunners looking to minimise their loss on the 28-year-old, having paid the Spanish club £17m for his services only a year ago.
Deportivo have had two bids rejected with the latest worth around £11m but manager Arsene Wenger is keen to trim his squad and all parties believe a compromise will be reached for Perez to depart.
His options have also diminished as a result of Arsenal’s reluctance to sanction a loan deal. Perez has attracted interest from a number of English clubs including Newcastle, Everton and, most recently, Swansea but that only extended to a temporary switch.
Everton are thought to be the most likely club to make a late rival offer with boss Ronald Koeman admitting following Monday’s 1-1 draw at Manchester City that the club were in the market for another forward but Perez would prefer a move back to Spain.
He is unhappy with his treatment at Arsenal having been restricted to just two Premier League starts in his debut season. Despite making just 21 appearances for the club, he scored in every competition and registered a Champions League hat-trick against Basel back in December.
Perez is pushing for a move but Alex Oxlade-Chamberlain’s future is less clear with further talks planned over a new Arsenal contract in the coming days.