The Argentina international has been heavily linked with a summer switch to Old Trafford and the Dutchman has intimated that a bid could be imminent
Antonio Valencia, Ashley Young and Nani are the only recognised senior wide playes at the Dutchman's disposal leading into the 2014-15 campaign, and the trio have yet to fully prove themselves at Old Trafford.
Di Maria - who is reportedly surplus to requirements at Madrid following James Rodriguez's arrival from Monaco - appeared destined for Paris-Saint Germain, only for the French champions to end negotiations after being priced out of a deal.
The collapse of Argentine's proposed move to Parc des Princes has opened the door for United, and Van Gaal has dropped a major hint that the club could launch a bid for Die Maria due to a lack of depth out wide.
"At this moment, we have five No. nines and four No. 10s – and we don't have wingers to give us attacking width," the former Netherlands coach told reporters.
"Or, I should say, we don't have wingers of the highest level, like Ronaldo or Di Maria or somebody like that.
"So, I have to play in another way – and you have seen that already. I only buy when I think we need to buy – in the position that is necessary."
Left-back Luke Shaw and central midfielder Ander Herrera have already arrived at Old Trafford but Van Gaal is still eyeing reinforcements.
Netherlands international and Ajax defender Daley Blind is reportedly on Van Gaal's list of targets as he attempts to bolster his defence and the 63-year-old insists he would have no problem recruiting Dutch players.
"If they are at the level I want them to be, then I will sign Dutch players," he said. "Nationality isn't something that concerns me.
"But Dutch players are usually cheaper than players of other nationalities and they have usually been very well educated in the Netherlands, I believe.
"But they have to be of a level than can play well in the English Premier League. You have to ask if that is the case with every player."