Arsenal have already made two offers for the Argentine and are awaiting a response from the Dutch club after tabling a second bid worth £35m.
He has made more than 100 appearances for the Eredivise champions, showing his versatility by playing in four different positions since joining them from Defensa y Justicia in 2019.
He predominantly played as a centre-back last season despite being just 5ft 9in, but can also play at left-back, right-back, and defensive midfield.
New Man United boss Erik ten Hag worked with him during his time in the Netherlands and looks keen to reunite with him at Old Trafford.
The pair have won back-to-back titles together and the Dutch boss is said to be a big admirer of the versatile 24-year-old.
Ten Hag highlighted his ability to play in various positions when there were reports that left-back Nicolas Tagliafico nearly left Ajax two years ago.
The new United boss said: "In preparation, I will try Lisandro Martínez in that position. He has also played in midfield for us, but he is a defender."
"I find Lisandro Martinez an excellent player, he is actually starting material and this is why I talk with him a lot," he added.
"But he has a lot of competition with Daley Blind, Tagliafico and [Ryan] Gravenberch. I can only start 11 players."