Martinez has been putting pressure on Ajax to reach an agreement over a fee to sell him to Manchester United this summer.
The Premier League giants have already failed with two bids, worth €45m and €50m respectively, and are set to hold more talks with Ajax today.
Ajax are holding out for somewhere around €55m to €60m, but the club are already in the process of identifying the Argentina international’s replacement.
According to Dutch daily De Telegraaf, the Eredivisie champions are interested in getting their hands on Shakhtar Donetsk’s Matvienko.
The 26-year-old defender has a contract until 2025 with Shakhtar Donetsk and the club are prepared to sell him for around €15m.
Ajax are considering making a move for him as the replacement for Martinez, who is pushing for a move to the Premier League.
But the Dutch champions will come up against direct competition from Eredivisie rivals Feyenoord, who also want the Ukrainian.
With Martinez expected to move on this summer, Ajax are in a hurry to bring in his replacement as soon as possible.