Since the end of the last campaign, Perez has been linked with an exit from Arsenal having made just two starts in the Premier League since his arrival from Deportivo last August.
The Spaniard has not been short of offers, but it has been suggested that no teams has been prepared to meet Arsene Wenger's valuation of the player.
However, according to the London Evening Standard, the two clubs could come to a compromise with a fee of £14m potentially being enough to push through the transfer.
It has been claimed that the signing could be made official by the end of the week, with Deportivo keen to add extra firepower to their squad and Wenger eager to bolster his funds ahead of a possible late move in the market.
If Perez does depart the Emirates Stadium, he will leave the North Londoners having scored eight goals in nine starts and 12 substitute outings in all competitions.