The two English powerhouses are believed to be in a two-horse race for the 24-year-old, who impressed in a variety of roles under Erik ten Hag in Amsterdam.
Martinez garnered praise for his showings at centre-back and as a defensive midfielder under Ten Hag, and both the Dutchman and Mikel Arteta are said to be intrigued by the idea of using the Argentina international as a left-back.
Martinez remains under contract at Ajax for another three years, meaning that the Dutch giants are under little pressure to sell for a cut-price figure in the current transfer window.
Arsenal are already said to have had two bids rejected by Ajax for Martinez, but the Gunners have scheduled another meeting with the Dutch champions to discuss a deal.
Meanwhile, Man United - who are now thought to be above Arsenal in the race to sign Martinez - have tabled a £39.6m bid for the South American, but Ajax are holding out for a £43m fee.
However, both Arsenal and Man United have seemingly been handed a boost in their efforts to sign Martinez, as Sky Sports News claims that the centre-back has hold Ajax that he wants to play in the Premier League.
The report adds that Martinez informed Ajax of his stance during a recent meeting following his holidays, and his only intention for the summer is to secure a move to an English top-flight club.
Martinez is reportedly still weighing up his options as he enjoys the second part of his holiday before pre-season, and the defender can see the positives of working at both Arsenal and Man United.
The former Defensa man is supposedly fascinated by the idea of working under Gunners boss Arteta, but a reunion with Ten Hag unsurprisingly also appeals to him.
Martinez ended the 2021-22 season with one goal and four assists to show from 37 appearances in all tournaments, and he was crowned the club's Player of the Year while also winning his second Eredivisie title.
The Argentine cost Ajax £6.3m to sign from Defensa in the summer of 2019, and he has gone on to register six goals and six assists in 118 appearances for the Amsterdam giants since.
Meanwhile, Arsenal have already welcomed William Saliba back to bolster the heart of the defence, but Martinez could be used as a left-back if Nuno Tavares is sold on a permanent basis. body check tags ::