Recently-appointed head coach Erik ten Hag finally made his first addition earlier this week with the acquisition of Feyenoord left-back Tyrell Malacia.
However, Ten Hag has continually being linked with a reunion with two players who he worked with during his stint at Ajax.
Martinez has been identified as an important signing in the defence, the Argentina international capable of playing in the middle and on the left-hand side.
Meanwhile, Antony is regarded as a potential incoming on the right flank, adding another option for Ten Hag at a time when there has been uncertainty over the make-up of his attack.
United's bid to sign the latter of those two players has been held up by an injury to the 22-year-old, the recent suggestion being that they may delay an offer for a number of weeks.
Nevertheless, according to the Daily Record, Ajax have outlined their conditions if United intend to be successful with their drawn-out pursuit of both players.
The report claims that the Eredivisie champions are demanding a combined total of €125m (£106.1m) if they are to part ways with two key men.
Separately, it had been reported that Martinez was available for a fee in the region of £43m, an asking price which has attracted more than just United.
Arsenal are known to be monitoring the situation with Martinez said to be torn over whether to reunite with Ten Hag or join Mikel Arteta's project at the Emirates Stadium.
The 24-year-old is said to be in favour of a switch to the Premier League having spent the last three years with the Dutch outfit.
The Daily Record adds that both players have Martinez and Antony are keen for offers to be accepted for their signatures this summer.
However, Ajax remain in strong positions in both situations, the pair each having three years remaining on their contracts.
On Friday morning, Ajax completed the signing of Tottenham Hotspur winger Steven Bergwijn, using the funds which were generated from the sale of Sebastien Haller to Borussia Dortmund.