The Belgian international has been linked with United following the appointment of David Moyes as Sir Alex Ferguson's successor.
But the Toffees star has vowed to stay at Goodison Park. As reported by The Sun, Fellaini said: "My destiny lies at Everton, it's as simple as that.
"We're talking about one of the biggest clubs in England, the framework is in place and the manager's departure doesn't change anything.
"He got a good offer and I understand why he accepted it. But he never told me he planned to take me to United. Rumours are part of football and I take them with a pinch of salt."
Fellaini has a £23m buyout clause in his Everton contract, and Moyes was reportedly ready to trigger it to make the Belgium star his first Old Trafford signing.
The 25-year-old midfielder has spoken of his Champions League ambitions in the past, and once again reiterated his dream to play in Europe's premier club competition.
"I miss playing in the Champions League but we deserved to win a place in it this year," said Fellaini.
"We were unlucky Spurs had a good season as well. But it's clear I am very happy where I am. Everything else is waffle."
Roberto Martinez looks favourite to replace David Moyes at Everton, after reports claimed the Spaniard held talks with Toffees chairman earlier this week.
Everton finished the Premier League season in sixth this term, ten points off Arsenal in fourth place - the final qualifying spot for the Champions League.