Reports in Spain claimed that his relationship with Van Gaal had broken down, with the pair not having spoken in months.
But the goalkeeper rejected that notion out of hand during an exclusive interview with MUTV on Friday.
“Everything that has been written in the press about us not getting on is a lie,” said De Gea.
“We both want the best for the club and the team, and the stories are complete lies.”
After signing seven players in his first year at the club, Van Gaal is expected to make more additions in the summer.
But for many United fans, the Dutchman’s priority should be extending De Gea’s contract, which expires at the end of next season.
The 24-year-old Spaniard has rescued United on countless occasions this season.
Few would have thought he was capable of such performances when, at the start of his United career, he made a series of howlers. He thinks those days are firmly behind him, though.
“I think this is the best period of my career,” added De Gea, who has been linked with a??big-money move to Real Madrid.
“I am playing the best football that I’ve ever played.
“I’m really enjoying it at the moment and I’m just trying to improve with every training session and every game that goes by, giving 100 per cent and concentrating to the maximum. That’s the way I want to continue.”