The 28-year-old came into the Arsenal side after the restart, replacing the injured Bernd Leno, and performed brilliantly as the side lifted the FA Cup.
However, with the German now back from injury, Mikel Arteta intends to reinstate Leno as his number one and has been unable to give Martinez any assurances over game time.
Aston Villa have already lodged a £15million offer for the Argentine – which is short of Arsenal’s asking price – while Brighton have recently emerged as contenders for his signature.
Martinez will not be in the starting XI when Arsenal take on Fulham on Saturday in the first game of the new Premier League season, and his agent says the keeper’s desire to move is being driven by his hopes of being Argentina’s number one.
‘The most likely scenario is that Emi Martinez leaves Arsenal because he wants to play,’ the shot-stopper’s agent, Lucas Martinez Quarta, told TyC Sports.
Arteta was asked about the possibility of Martinez leaving at his pre-match press conference and hinted that the goalkeeper’s push for regular first-team football could prompt his exit.
‘We have some really good players in many different positions. Some of them are complicated and obviously, clubs come to us and they are interested in our players,’ said the Spaniard.
‘It is very difficult to promise players game time or to be the first choice. It is part of this period in the market. We try to manage the situation as well as we can, all the time counting on what the players’ expectations are, what we can achieve with them as a club and we are making decisions towards that.’
Arsenal are believed to be interested in signing Brentford goalkeeper David Raya as Martinez’s replacement, though the Championship club insist he is not for sale.