The Argentina international scored once and provided four assists in 36 appearances in all competitions for Ajax last term, playing a key role in their Eredivisie success.
Man United and Arsenal continue to be strongly linked with the 24-year-old, who still has three years left to run on his current deal in Amsterdam.
With that in mind, Sports Mole has taken a closer look at Martinez, who is believed to be keen to make the move to the Premier League during this summer's transfer window.
Martinez had spells with Club Urquiza and Club Libertad during his youth career before moving to Newell's Old Boys, spending three years in their academy before debuting for the first team in 2017.
The defender only made one first-team appearance for La Lepra, though, before joining Defensa y Justicia on a permanent basis following a successful loan spell at the club during the 2017-18 campaign.
Martinez represented Hawk on 58 occasions in all competitions before joining Ajax in 2019, penning a four-year contract with the Dutch outfit with the option of an additional year.
The South American made his debut for the Amsterdam giants in the 2019 Johan Cruyff Shield against PSV Eindhoven, and he has been an important player for Ajax during his three seasons at the club.
Martinez has played 74 times in the Eredivisie since his arrival, while he has featured on 120 times in total, helping the club win back-to-back league titles and the KNVB Cup in 2021.
Last season, the defender made 36 appearances in all competitions, contributing one goal and four assists in the process, with 24 of those outings coming in the league.
Martinez also played eight times in the Champions League, as Erik ten Hag's side reached the last-16 stage of the competition before losing to Benfica.
The Argentine played as a centre-back for Ajax last season, but he is also capable of featuring at left-back and in central midfield, with his versatility believed to made him an even more attractive proposition for both Man United and Arsenal.
Martinez has also featured on seven occasions for Argentina, including 62 minutes of their last match in June - a 5-0 win over Estonia in a friendly, but he was an unused substitute for their 3-0 win over Italy in the Finalissima at the start of last month.
According to Italian journalist Fabrizio Romano, Arsenal are currently ahead of Man United in the race to sign the defender during this summer's transfer window.
"My understanding is that these are two negotiations at different stages: Arsenal have already submitted official offers up to €40m (£34.2m) plus add-ons for Martinez, while Manchester United are currently busy with Tyrell Malacia and Frenkie de Jong, but have had contact with Lisandro's agents," Romano wrote in his column for Caught Offside.
"The player is so far open to negotiate with both clubs. Arsenal are insisting a lot this week because Arteta is understood to be a big fan of Lisandro, considered a versatile player with top team skills. For now, the Gunners' interest is more advanced, but this still looks like it could be an open race."
However, Dutch journalist Marcel van der Kraan has said that the player is keen to link up with new Man United boss Ten Hag at Old Trafford next term.
"Martinez is very high on Erik ten Hag's wishlist, so I expect big developments in the 24 or 48 hours," he told De Telegraaf. "Martinez will also have his hopes pinned on United, who are an absolute top club for him.
"Ajax will really cash out for Martinez and go to €45m (£38.7m)-€50m (£43m), but that is the advantage if two clubs bid, as we saw with Lyon and Manchester United, then it suddenly goes higher."
Ajax are not under any firm pressure to sell Martinez, and the fact that he still has three years left to run on his contract has placed the club in a strong position, but it seems likely that he will move to the Premier League before the end of the summer transfer window.