Both Premier League clubs have been repeatedly linked with a move for the Brazilian playmaker during the current transfer window, but, according to recent reports from Italian publication Tuttosport - brought to our attention by talkSPORT - it is Milan who are frontrunners to land Douglas from Shakhtar Donetsk.
The same source suggests that the 23-year-old is seeking to depart the Donbass Arena in the near future due to the current conflict that is engulfing the region, with Shakhtar supposedly valuing Douglas at a minimum of £30 million.
Big price tag
Such an extravagant price tag seems wholly unrealistic and somewhat unjustified given that the 23-year-old has no experience of European football outside of Ukraine, although Shakhtar certainly have form when it comes to making huge profits on talented Brazilian midfielders.
In February 2013, the reigning Ukrainian Premier League champions sold Willian to Anzhi Makhachkala for the same price, with the former Corinthians starlet going on to move to Chelsea just a few short months later following a brief flirtation with London rivals Tottenham.
AC Milan are evidently eager to make somewhat of an impact during this particular window. The 2013/14 campaign - which saw the Rossoneri eventually finish eighth in Serie A after the sackings of Massimiliano Allegri and Clarence Seeforf - was dismal even by the club's recent low standards and new manager Filippo Inzaghi is understandably keen to minimise the chances of a repeat.
The long overdue re-build at the San Siro is already well underway, of course, with Pablo Armero, Michael Agazzi, Alex, Adil Rami, Michelangelo Albertazzi, Jeremy Menez, Diego Lopez all having already signed on in recent weeks.
Douglas would be another valuable addition to Inzaghi's first-team squad, although it seems doubtful that Milan would be willing to immediately meet such a hefty asking price.
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Premier League move?
It is as of yet unclear if either Manchester United or Arsenal intend to make a concrete offer to try and swing the race for Douglas back in their favour, although it again has to be considered extremely doubtful that the latter would be content to spend such a large sum on a player whose position is already well filled in Arsene Wenger's current squad.
With Jack Wilshere, Alexis Sanchez, Santi Cazorla, Mesut Ozil, Alex Oxlade-Chamberlain and veteran Tomas Rosicky all available to occupy an attacking position behind the lone striker, it could certainly be argued that the Gunners would be better served focusing their attentions on the pursuit of a more combative, defensive midfield presence.
Manchester United, meanwhile, look to be getting increasingly desperate to complete new signings as the clock quickly ticks down towards the deadline.
Despite the first summer under the management of Louis van Gaal seeming to promise a hatful of top-quality and expensive new arrivals, so far the Red Devils have only been able to complete deals for midfielder Ander Herrera and England left-back Luke Shaw.
Van Gaal's seemingly relentless pursuit of Real Madrid's Angel di Maria would suggest that he is open to strengthening his attacking midfield options further, although the Argentine is unquestionably the superior target.