Recent reports have claimed that the new boss has no plans to include the Belgium international in his team after he failed to make an impact during his debut season at Old Trafford.
The 26-year-old was one of former manager David Moyes's summer signings last year, but a wrist injury and lack of form prevented the midfielder from living up to his reported £27m price tag.
According to the Manchester Evening News, Van Gaal has not told executive vice chairman Ed Woodward to sell Fellaini before he arrives at Old Trafford after the World Cup, and the midfielder is said to be determined to fight for his place.
Fellaini poured doubt over his future while in Brazil with his national team by suggesting that he is unsure whether he will be at United next season.
Reports have claimed that Italian side Fiorentina are keen to sign the midfielder.