The Mirror says Atletico keeper Jan Oblak is out of contract at the end of the season and is yet to signal that he intends to sign a new deal with the La Liga giants. As a result, Diego Simeone's club are assessing alternative options and Martinez is well placed amongst them.
Atletico will even consider selling Oblak in January rather than risk losing him on a free six months later.
If he goes, then Martinez is seen as a player who could fill any void left by Oblak by compatriot Simeone, although Villa won't want to lose the Argentina international.
The chance to play Champions League football would make a move to Madrid appealing for the keeper, however, and could put Villa in a tricky position.
Martinez has established himself as one of the Premier League's top shot-stoppers since joining Villa in a £20million deal from Arsenal back in September 2020 and is also now Argentina's No.1 goalkeeper.