The Lilywhites are starting to plan for life without long-serving number one Hugo Lloris, whose contract at the Tottenham Hotspur Stadium has fewer than 18 months left to run.
Lloris turns 37 in December and has come under criticism for a decline in performances this term, and a new number one is expected to be high on the Tottenham agenda this summer.
Fraser Forster has held the fort well during Lloris's recent absence with a knee injury, but at 34 years old, the ex-Southampton goalkeeper is not a long-term investment either.
Meanwhile, academy graduates Alfie Whiteman and Brandon Austin have made just one first-team appearance between them, with the former making his debut in November 2020.
A plethora of well-renowned goalkeepers have been linked with moves to North London, including Martinez, despite the Argentina World Cup winner's Arsenal connections.
According to journalist Gaston Edul, Tottenham have a concrete interest in bringing Martinez back to the capital and could make an offer for the 30-year-old in the coming weeks.
Martinez has shone for the Lions since joining in 2020, but Villa are said to be open to appropriate bids for the South American, who is under contract at Villa Park until 2027.
Martinez, who has been reunited with ex-Arsenal coach Unai Emery in the West Midlands, arrived for just £15.4m three years ago, and Villa could command as much as £40m to sell him this summer.
The World Cup winner was on the books at Arsenal for 10 years between 2010 and 2020, but he spent the majority of his time in North London on the bench and made just 38 appearances for the senior team.
Following a serious knee injury to Bernd Leno, Martinez made his Arsenal breakthrough at the end of the 2019-20 season and won the FA Cup and Community Shield before departing.
The Argentina international has now brought up a century of appearances for Aston Villa, keeping 33 clean sheets, but he was blasted by Emery for going up for a corner in last month's 4-2 loss to Arsenal, allowing Gabriel Martinelli to score into an empty net.
"Today, I am very, very disappointed. I am embarrassed about the last goal. I have never told my 'keeper to go forward. It's not the spirit. We have to keep our mind clear and be smart," Emery told BBC Sport.
"I have never told my 'keeper to do it. Today he decided it was his decision. I didn't tell him. He knows now [not to do it]."
Everton's Jordan Pickford is also thought to be a prime target of Tottenham's to replace Lloris, while Dean Henderson, David Raya, Robert Sanchez and Giorgi Mamardashvili have also been mentioned as possible targets.