United have told Ajax they are willing to pay €50 million for the 24-year-old, although they are holding out for more amid further interest from Arsenal.
Negotiations with the Dutch side are being played out against a backdrop of uncertainty over the move for De Jong.
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Sources have told ESPN that dialogue remains ongoing despite public claims from Barcelona that the midfielder is not available for a transfer but there remains uncertainty at Old Trafford about whether a deal is possible.
United have agreed to an initial fee of around €65m for De Jong but sources have told ESPN that are still significant hurdles to overcome.
They include an issue around wages owed to the Dutchman after he agreed to take a pay cut to help the Spanish side through the COVID-19 pandemic on the understanding the money would be repaid over the remainder of his contract, which runs until 2026.
Performance-based add-ons are also yet to be agreed.
Sources have told ESPN that there is a feeling at United that a deal for Martinez is now more attainable and that the Argentinian, who can play in defence and midfielder, could be convinced to snub Arsenal and move to Old Trafford if Ajax show a willingness to compromise over the fee.
United fly to Bangkok on Friday to start their preseason tour of Thailand and Australia with left-back Tyrell Malacia as the only new face in the squad. Christian Eriksen is still on course to sign a three-year deal but is not expected on the flight while his move is wrapped up.
According to sources, Inter Milan's interest has cooled after they landed Romelu Lukaku on loan from Chelsea and the Argentinian's representatives are now keen to strike up interest from Premier League clubs including United.
United insist any interest in Dybala does not change their stance that Ronaldo, who is keen to leave the club this summer, will not leave Old Trafford.
Meanwhile, sources have told ESPN that United hold an interest in striker Brian Brobbey.
The 20-year-old scored seven goals in 13 games on loan at Ajax from RB Leipzig last season. United have already been in contact with the German side about a deal and there is hope a fee of under €20m can be agreed.