Manchester United's summer transfer budget is reportedly £100m before sales, with the club needing to part with unwanted players in order to boost the money available to Erik ten Hag.
A deal for De Jong could cost in the region of £70m, and according to The Sun, Ajax want £69m for Antony, which would take the club comfortably past their £100m summer budget.
The report, though, claims that the club's owners are prepared to hand the new head coach more money if he moves on some of their unwanted players this summer.
The 20-time English champions are also said to be desperate to sign a new centre-back, while a forward could also arrive at the club before the end of the transfer window.
However, there will not be much change left over from £100m once De Jong's transfer has gone through, making player sales vitally important for Man United this summer.
Anthony Martial could also be on his way out of Old Trafford this summer following an unsuccessful loan spell at Sevilla in the second half of the 2021-22 campaign.
Donny van de Beek is heading back to the club after a loan spell at Everton, and the Netherlands international will allegedly be given the chance to kickstart his Man United career next term.
The Red Devils are expected to have 15 first-team players at their opening pre-season session on Monday, as Ten Hag officially starts work as head coach.
Man United will open their pre-season against Liverpool on July 12, while they will also face Melbourne Victory, Crystal Palace, Aston Villa, Atletico Madrid and Rayo Vallecano ahead of the new Premier League season.
The Red Devils will play five league fixtures in August, facing Brighton & Hove Albion, Brentford, Liverpool, Southampton and Leicester City in the opening month of the campaign.