United are set to sign the Argentina international after agreeing a fee of around €55 million. Martinez, who has stopped training with Ajax ahead of his transfer, rejected interest from Arsenal in order to seal a move to Old Trafford.
Sources have told ESPN the deal will be subject to international clearance and Martinez receiving a visa, but there is hope he will be able to travel to Australia where Erik ten Hag's squad are preparing for the new season.
United face Melbourne Victory at the MCG on Friday before a game against Crystal Palace at the same venue on Tuesday. Ten Hag and his players are then due to fly to Perth for the final game of the tour against Aston Villa on July 23.
After wrapping up a move for Martinez, United will continue their attempts to sign Frenkie de Jong from Barcelona. The two clubs have a broad agreement on the fee, add-ons and the payment structure, but sources have told ESPN that De Jong still needs to be convinced to move.
United remain sure the Netherlands international is open to joining the club but, according to sources, his representatives are still trying to encourage Paris Saint-Germain and Chelsea to join the bidding.
De Jong would rather join a Champions League club if he has to leave Barcelona, although his preference is to remain at Camp Nou despite the LaLiga side's insistence he has to move to help the club solve their financial issues. There is also an issue of wages that total more than €20m that Barcelona owe De Jong.
Meanwhile, sources have told ESPN that United still expect to sign Christian Eriksen on a three-year deal. The Denmark midfielder has verbally agreed to join the club, but needs to undergo a thorough medical after suffering a cardiac arrest on the pitch a year ago at the European Championship.