According to BBC Sport, the Red Devils will pay £59.7 million for Di Maria, a price which will smash the previous British transfer record of £50 million that Chelsea splashed out to bring Fernando Torres to Stamford Bridge back in 2011.
The same source reports that Di Maria will undergo a medical ahead of the move on Tuesday morning, although the deal obviously will not be confirmed in time for the player to feature in Manchester United's Capital One Cup second round tie against MK Dons tonight.
A first-team bow against newly-promoted Burnley at Turf Moor next weekend seems far more likely, with Di Maria having missed Real Madrid's recent 2-0 win over Cordoba.
Saga at an end
Such an agreement will finally bring Manchester United's pursuit of the versatile playmaker to an end, with this particular transfer saga having been raging for several months now.
Despite performing a key role in Real's Champions League final victory against rivals Atletico back in May, Di Maria appears to have found himself somewhat surplus to requirements at the Santiago Bernabeu.
In typical Florentino Perez style, Real - who finished three points behind Los Rojiblancos in La Liga last year - looked to make a significant impact in this summer's market, with impressive World Cup duo Toni Kroos and James Rodriguez arriving from Bayern Munich and Monaco respectively.
Manchester United have endured another difficult period during the current transfer window. Although the reputable and experienced figure of Louis van Gaal is now at the helm, the club - who have not signed a prominent player from the continent since Juan Sebastian Veron was bought from Lazio in 2001 - have struggled to attract the big names to Old Trafford.
A failure to qualify for the Champions League under the putrid reign of David Moyes has not helped matters, although it seems to be executive vice-chairman Ed Woodward who is once again receiving the bulk of criticism from understandably disgruntled supporters.
While new signings are unquestionably required at Manchester United after their disappointing start to the new Premier League campaign, it could be argued that Di Maria's capture will not solve the most glaringly obvious problems in Van Gaal's current squad.
The 26-year-old will bring pace and skill in abundance, of course, but the Dutchman remains desperately in need of a new midfield enforcer and at least one new world-class defender to compete alongside the likes of Chris Smalling, Phil Jones and young Tyler Blackett.