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The Belgian, who David Moyes brought to Old Trafford for a fee of £27.5 million, was the subject of transfer speculation this summer.
But the 26-year-old says he was never told to leave United by Van Gaal, who simply warned him of the competition for a first-team place that faces him.
"I talked to Van Gaal and he has never said that I had to leave. He said I had a lot of competition but that I got the chance to prove it [that I deserve to play],' Fellaini told Sport Wereld.
"I have known difficult moments last season but there is a stronger player afterwards. I have confidence in myself and in my game again.
"I played a good World Cup and also during the preparation, I was good. It is unfortunate that this injury is for now just a spanner in the works, but at the end of the month I will be back."
The 21-year-old recently rejoined former club Crystal Palace on a temporary deal and Neville has backed the move as the best thing for Zaha's United future.