Additionally, personal arrangements have been agreed upon with Martinez, 24, and United is expecting he would travel with them to Australia for their preseason tour.
Richard Arnold, the chief executive of United, and John Murtough, the football director, headed to Amsterdam to negotiate the agreement with Edwin van der Sar, the chief executive of Ajax and a former United goalkeeper.
Martinez has drawn interest from Erik ten Hag's team, but the United manager has the upper hand.
According to The Athletic, United was in discussions with Ajax about signing Martinez.
Martinez reportedly informed the Eredivisie champions that a transfer to the Premier League is the only option he would consider this summer.
It was agreed upon when Ajax renewed his contract in October that they would not obstruct him if such a chance presented itself.
Martinez was said to be a target for Arsenal as well, but the left-sided center-back is believed to have been more intrigued by the chance to reunite with Ten Hag, who managed him at Ajax.
Martinez appeared seven times for Argentina and played 36 times for Ajax last season.
United plays Melbourne Victory on Friday, then Crystal Palace on Tuesday, and Aston Villa on Saturday, all while in Australia.
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