The 27-year-old worked his way back into Ole Gunnar Solskjaer's plans last season, making 48 appearances across all competitions including 23 Premier League starts.
"I want to stay here – that's my desire. I don't want to leave. As I've always said, I want to be an important player and win trophies for this club," Fred told FourFourTwo.
"[Van de Beek's arrival] means we're getting stronger and that's good for everyone at United. We need more players for this season because it will be even more demanding: the calendar is crammed and we need a strong squad to compete for every title.
"When you play at a big club, there will always be competition – I'm used to it. It's been like that from day one at United."
United's first game of the new season does not come until September 19, when they host Crystal Palace at Old Trafford.