Antonio Valencia, Ashley Young and Nani are the only recognised senior wingers at Van Gaal's disposal leading into the 2014-15 campaign, and the trio are yet to fully convince in Manchester.
Di Maria - surplus to requirements at Real Madrid following James Rodriguez's arrival - appeared destined for Paris-Saint Germain, only for the French champions to end negotiations after being priced out of a deal.
PSG's decision not to sign Di Maria has opened the door for United, who have a long-standing interest in the Argentina international.
And talk of a possible bid for the 26-year-old looks set to intensify after Van Gaal said the club were in the position to break their transfer record.
"It is a strategy of Manchester United to do that," the Dutchman said.
"At this moment, we have five number nines and four number 10s – and we don't have wingers to give us attacking width.
"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 defensive stocks and the 63-year-old said 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."
