Perez, 28, joined the Gunners for a fee of £17.1million ahead of the 2016/17 season but is expected to return to La Liga in the coming weeks, after making only 11 appearances in the Premier League.
The striker’s agent has consistently hinted at a return to Spain and Deportivo are determined to bring their former player back to Estadio Riazor.
AS claim Deportivo have offered Perez a whopping ten-year contract, with a view to the Spaniard becoming technical secretary upon his retirement.
It’s believed a fee of around £9-11million could convince Arsenal to allow Perez to leave off the back of an immensely frustrating spell in England.
The attacker is tied into a deal at the Emirates until the summer of 2021 but Arsene Wenger is prepared to sanction a move.
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Fenerbahce have also expressed an interest in Perez but the player would prefer a return to Deportivo.