The Dutchman has targeted Arsenal club captain Thomas Vermaelen and Borussia Dortmund's German World Cup winner Mat Hummels as he aims to hit the ground running in the race for the Premier League title.
But Barcelona boss Luis Enrique has also enquired about both players as he looks to make an immediate impact after taking over as Nou Camp manager in the summer.
Vermaelen could be available for a knockdown £10 million after being told by Gunners boss Arsene Wenger that he can't guarantee the Belgian a regular starting place.
United have been in negotiations to sign Hummels since Van Gaal was appointed but Dortmund are reluctant to sell. If they do it will only be for a fee in the region of £25 million to £30 million.
Van Gaal has made the signing of an established central defender a priority after seeing Nemanja Vidic and Rio Ferdinand leave.
Van Gaal has targeted Arsenal's Thomas Vermaelen but Barcelona are also seeking his services [AFP/GETTY]
He also wants to bring in a ball winning midfielder with United continually linked with Juventus hardman Arturo Vidal while AC Milan's Dutch international Nigel de Jong is a cheaper option.
Off the field the former Ajax, Barcelona, Bayern Munich and Holland manager has already made his mark, adding almost £250 million to the value of the club.
Since being appointed United's value on the New York Stock Exchange has soared. A week ago at its peak the club's shares were worth around £250 million more than when David Moyes was sacked.
Over the last few days they have fallen slightly after United's owners, the Glazers, cashed in on five per cent of their shareholding for £89 million.
The family ownership is now 85 per cent with City analysts believing more shares will be sold over a period of time.