The former Premier League champions, who finished seventh last year, have been consistently linked with the Real Madrid and Argentina winger.
However, according to Spanish football pundit Balague, United are yet to register an offer for the 26-year-old, who could be worth anything from £50 million upwards according to reports.
Interestingly, Di Maria started the first leg of Madrid's Spanish Super Cup against Atletico Madrid on the bench.
With Real's star-studded line-up, they are said to be willing to listen to offers for the Argentine and United boss Louis van Gaal has previously commented that his team lack a player of Di Maria's class out wide.
On di María. As of today, there has been no offer whatsoever for the player by Manchester United. None so far.— Guillem Balague (@GuillemBalague) August 21, 2014
Manchester United did confirm a new signing in Marcos Rojo yesterday, although they are yet to sign a new forward or attacking midfielder this summer.
Di Maria has long been linked with a move to Old Trafford but Paris Saint-Germain had also been touted as potential suitors earlier this summer.
Real Madrid boss Carlo Ancelotti has also confirmed that the winger wants to leave the club.
Ancelotti: "Di María has asked to leave & rejected offer from club. [But] if he does not find future solution he stays no problem"— Dermot Corrigan (@dermotmcorrigan) August 21, 2014
If United are genuinely interested in the 26-year-old, however, the longer they leave a bid, the higher Madrid's asking price may be.
Van Gaal's side travel to Sunderland for their second Premier League clash of the season on Sunday afternoon.