Martinez joined Villa from Arsenal in 2020 - following eight years in North London where he was loaned out six times.
Emi Martinez is wanted by Manchester United and Barcelona, say reports in Argentina
And he emerged as one of the best keepers in the league, also cementing his place as Argentina No1 before their 2022 World Cup win.
But Martinez - whose contract expires in 2029 after extending it in the summer of 2024 - appeared to hint that he is leaving the club.
He was seen tearfully waving to fans following Villa's 2-0 home win against Tottenham - suggesting he is preparing for an exit.
And according to Argentine TV channel DSports, United and Barca are both interested in signing Martinez and the keeper has offers from both.
United No1 Andre Onana has suffered inconsistent form since arriving from Inter Milan in 2023 in a deal worth £47.2million.
Old Trafford legend Wayne Rooney even suggested the club should re-sign David de Gea - who left on a free with Onana replacing the Spaniard.
Marc-Andre ter Stegen is still Barca's main stopper but the German has played only seven times this season due to a horror knee injury.
Former Arsenal keeper Wojciech Szczesny - who joined in 2024 after coming out of retirement - has played 30 times in Ter Stegen's place.
The 35-year-old Pole's contract expires at the end of the season - after Barca were crowned LaLiga champions - but there is an option to extend.
Villa boss Unai Emery, meanwhile, remained tight-lipped on Martinez's future despite the World Cup winner's emotional gesture to fans.
Emery said: "We will see. Of course, it is the last match (of the season) here, and I don't know. We will see about the team, the players.
"Of course, they are responding on the field, at the moment they are responding and they are so, so focused in how we are preparing and playing each match."
But Sky Sports pundits Jamie Redknapp and Roy Keane seem more convinced that it was a goodbye from Martinez.
Redknapp said: "What a signing he has been. Amazing player, great goalkeeper, but it looks like he was waving goodbye.
"Trying to find someone to fill that void will be very difficult."
Keane added: "He has been a good character, some people like him. He can be annoying at times with some of his antics.
"But he has been a great signing for them, he'll be a big loss as it does look like he his saying his final goodbyes."
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