The Red Devils boss is hoping to reunite with his Dutch compatriot rather than sign a weaker midfielder in the summer transfer window, and would happily wait until January.
The United manager is a huge fan of Strootman and the club will monitor the Roma midfielder’s recovery from a serious knee injury in hopes of trying to sign him in the new year.
Van Gaal has described the United squad as "not balanced" and the Dutchman wants to sign a box-to-box central midfielder to bolster his side — but he is happy to wait to land a top-class target.
MORE: Biggest summer transfers | Soccer's beautiful fans
Arturo Vidal has been constantly linked with a move to Old Trafford. While Van Gaal has declared his admiration for the Juventus star, club officials have been keen to play down any prospect of signing him this summer.
Interest in Germany international Toni Kroos cooled before he joined Real Madrid from Bayern Munich, while interest in Real midfielder Angel di Maria has faded, with the Argentine likely to join Paris Saint-Germain if he leaves the Spanish capital.
William Carvalho of Sporting Lisbon and Everton's James McCarthy have also been considered by Old Trafford officials, while Netherlands international Memphis Depay could be a target next summer — but not this year.
Van Gaal, however, is adamant that the club should not panic buy, and is more than happy to work with his current midfield options come the start of the new Premier League season.
That means the likes of Tom Cleverley look set to initially be given a far bigger role to play at Old Trafford than many may have expected. The former Wigan Athletic loanee, something of a scapegoat during the David Moyes era, has been given the captain's armband at times in preseason and is one of a few of the club's fringe stars with a point to prove in 2014-15.
Van Gaal worked closely with Strootman, 24, in his previous role as Netherlands coach and believes his compatriot is perfectly suited to the Premier League and the style he wants to implement at Old Trafford.
Ed Woodward, United’s executive vice chairman, is eager to provide Van Gaal with additions in the transfer market and has claimed the club is financially strong enough to break the world transfer record.
But Van Gaal is understood to have told Woodward to focus his attention on signing a center back — Mats Hummels would be his dream signing, though a move for Arsenal's Thomas Vermaelen is eminently more realistic at this stage — rather than chase high-profile attacking players.
United started the summer with a 190 million euro budget and has spent almost 76 million euros so far to bring Luke Shaw and Ander Herrera to Old Trafford.