Martinez won Ajax's 2021-22 Player of the Season award for his exploits in the heart of the backline, and journalist Gaston Edul claims that the centre-back's preference would be to reunite with Erik ten Hag at Old Trafford.
Mikel Arteta was thought to be keen on the idea of using Martinez as a left-back given his qualities on the ball and Nuno Tavares's struggles to adapt to the Premier League last season.
Furthermore, with Scotland starlet Aaron Hickey now a confirmed Brentford player, Arsenal will need to widen their search for full-back reinforcements in the coming weeks.
Here, Sports Mole looks at three other players Arsenal could target who could fill the Martinez role in Arteta's XI.
Alex Grimaldo
Benfica left-back Alex Grimaldo could be one of the bargain buys of the summer for potential suitors, with the defender still only 26 years old and due to become a free agent at the end of next season.
The former Spain Under-21 international is a serial winner with the Portuguese giants, boasts plenty of experience on the European stage and has totalled 19 goals and 50 assists in 246 outings for his current side.
Grimaldo's exploits with Roger Schmidt's side will likely lead to interest from a number of clubs this summer, namely Barcelona, where he learned his trade as a youth player before making the move across the Iberian Peninsula.
Arsenal would certainly not need to break the bank to sign him, and a fee of €7m (£5.9m) could supposedly be enough, which would allow Edu and co to prioritise their big-money moves in other areas of the field.
Oleksandr Zinchenko
Manchester City's Oleksandr Zinchenko was considered one of Arsenal's top summer targets during the earliest days of the transfer window, with Arteta knowing the 25-year-old well from his Etihad era.
However, speculation has cooled dramatically over the past few weeks, with the champions also at risk of losing Chelsea-linked Nathan Ake and Benjamin Mendy still suspended by the club.
The chance to reunite with Arteta and Gabriel Jesus may come into Zinchenko's thinking over the coming weeks, and the Ukraine international only has two years left to run on his deal in Manchester.
Zinchenko's capabilities in the middle of the park for Ukraine will certainly come in handy for Arsenal, who could still attempt to bolster their engine room ranks before the window shuts, and it would be no surprise to see the Gunners reignite their interest in the Man City man if Marc Cucurella's proposed switch to the Etihad comes to fruition.
David Raum
Hoffenheim's David Raum took to the Bundesliga like a duck takes to water, and the Germany international proved to be one of the standout free transfers of the 2021 summer window.
Raum ended his 15-year association with Greuther Furth to head for the Rhein-Neckar-Arena and ended his first season in the top flight with three goals and 13 assists from 32 appearances - only Thomas Muller set up more goals.
The 24-year-old's exploits have helped him break into the Germany setup under Hansi Flick, and he was strongly linked with a move to Manchester United before the Red Devils swooped for Tyrell Malacia.
With no competition from Old Trafford, Arsenal should not turn their noses up to a bid for Raum, and director Alexander Rosen has admitted that the defender could be allowed to leave for the right price this summer.