The 24-year-old enjoyed a strong 2021-22 campaign for his Dutch club, making 37 appearances in all competitions, contributing one goal and four assists in the process.
Martinez still has more than three years left to run on his contract in Amsterdam, but there has been speculation surrounding his future in recent weeks, with Barcelona believed to be keen to bring him to Camp Nou in the upcoming market.
According to The Telegraph, there is also genuine interest from Man United, with incoming boss Ten Hag keen to sign the Argentina international for his new club.
The report claims that Martinez could be available for a fee in the region of €30m (£25.4m), which is seen as an attractive deal by the 20-time English champions.
The South American has made 119 appearances for Ajax since arriving from Defensa y Justica in 2019, contributing six goals and six assists in the process.
Martinez scored once and provided three assists in 24 appearances during the team's title-winning 2021-22 Eredivisie campaign, while he also featured eight times in the Champions League.
Ten Hag is allegedly keen to sign a 'quick' centre-back this summer, with the Dutchman look to change the team's playing style during the 2022-23 campaign.
Harry Maguire has been a part of a Man United defence that has conceded 56 Premier League goals this term, and his performances in 2021-22 have been widely criticised, while Raphael Varane has struggled with injury problems during his first campaign at the club.
The Red Devils will not play Champions League football next season, with the club instead battling West Ham United for sixth position in the Premier League table, which would secure a spot in the 2022-23 Europa League.
Ralf Rangnick's side are two points clear of seventh-placed West Ham ahead of Sunday's clash with Crystal Palace, with the Hammers finishing their campaign away to Brighton & Hove Albion.
Man United are also expected to sign a new central midfielder and forward this summer, with Barcelona's Frenkie de Jong and Benfica's Darwin Nunez strongly linked with moves to the club. body check tags ::