The 32-year-old Argentina international, who has amassed 52 senior caps and famously lifted the World Cup in 2022, is being considered as a potential replacement for Andre Onana.
While Onana is still expected to remain at Old Trafford next season, a series of high-profile mistakes have prompted speculation that United could look to upgrade their goalkeeping department.
Martinez, widely regarded as one of the best goalkeepers in world football, is said to be open to the idea of joining United.
The former Arsenal shot-stopper joined Villa in 2020 and has since established himself as a key figure at Villa Park.
A move to Manchester would mark a return to the Premier League spotlight for the Argentine, who helped Villa to a top-four finish last season.
United may face competition, however. Reports indicate there is significant interest in Martinez from Saudi Arabia, where a lucrative move could tempt the experienced keeper.
Nonetheless, United are believed to hold an edge in the race for his signature, although the details of that advantage remain unclear.
Martinez would likely command a fee in the region of 30-40 million pounds, a figure considered reasonable given his pedigree and consistent performances.
Manchester United and Chelsea are reportedly exploring blockbuster moves that could see Alejandro Garnacho and Christopher Nkunku switch clubs, as both players seek fresh starts after turbulent seasons.
Manchester United have intensified their efforts to sign Brentford forward Bryan Mbeumo, submitting a package worth over 60 million pounds as part of their ambitious summer rebuild.
Manchester United winger Alejandro Garnacho has drawn attention during the off-season after posting a photo of himself on social media wearing an Aston Villa shirt.
La Liga giants Barcelona's reported interest in signing Manchester United's Marcus Rashford only extends as far as them being able to sign the winger on their terms.
