The Netherlands coach, who will take over at Old Trafford after the World Cup, has already outlined his desired transfer targets ahead of the summer window - including the likes of Kevin Strootman and Toni Kroos.
Juan Mata broke the club's transfer record when he joined from Chelsea in January for £37.1 million - going on to score six goals in 15 appearances - but some reports have suggested he could be sold as part of Van Gaal's summer upheaval.
De Gea, however, feels the fellow Spaniard gives his side another dimension and is determined to see him stay.
"I would not sell Juan Mata. He is very important player for us," he told Movistar.
"We have taken a qualitative leap with him and he has adapted very well".
De Gea has been vocal in recent days, admitting he has been trying to lure Barcelona star Cesc Fabregas to United before revealing he would love to see Andres Iniesta join the club.
The goalkeeper will hope to make his Spain debut, potentially alongside Mata, Iniesta and Fabregas, against Bolivia on Friday.