The 28-year-old has been at Arsenal since 2010 but has largely been an understudy or out on loan, playing for six other clubs on short-term deals.
However, he was given the chance to play regularly after the coronavirus hiatus, due to an injury to first choice Bernd Leno, and he grabbed it with both hands.
The Argentine was in excellent form as Arsenal hit their stride towards the end of the campaign, winning the FA Cup and he remained in goal to win the Community Shield last week, despite Leno being back fit.
Gunners boss Mikel Arteta now has a big decision to make between keeping faith in Martinez or handing Leno the gloves. It has now reached a situation that neither would be happy to accept the role of understudy to the other, so one is likely to leave before the end of the transfer window.
If Leno returns to the starting XI then Emery is keen to take Martinez to Villarreal, reports the Telegraph, where he works with goalkeeping coach Javi Garcia, who was also with Emery and Martinez at Arsenal.
Schalke have also been credited with an interest in Martinez, as have Aston Villa so he is not short of options if he decides to bring his long spell in north London to an end.
After his lengthy service to the club, the Telegraph reports that Arsenal may be willing to accept as little as £7m for the goalkeeper, despite still having two years left on his contract.
This would only be if Martinez makes it clear he wants to leave, though, as Arsenal would rather keep hold of the impressive stopper and are keen for him to sign a new deal.
Arteta wants to keep hold of both ‘keepers and see them compete for the number one spot.
‘I’m delighted to have both of them,’ the Spaniard said before the Community Shield. ‘But they both know that on the first day of pre-season, you start again and fight for your place and show us who is the one that deserves the chance to start.
‘I don’t want to keep them both happy, I want the one that is not playing to be upset.
‘But upset and then challenge the next player to make him better, or if not, earn his place to do that. It’s not easy to do that.
‘I personally don’t see any different with goalkeepers to full-backs. They know that, I’ve been really clear with them and hopefully they can make each other better and hopefully the team better.’