The midfielder said he was pursued by Arsene Wenger in the summer and acknowledges he has been frustrated with his performances at Old Trafford this season.
Goal reported in June that Arsene Wenger was plotting a 22 million pound bid for the then-Everton man, but was only willing to offer a 70,000-pound-a-week salary - less than his earnings at Goodison Park.
Fellaini eventually reunited with David Moyes at Old Trafford on deadline day, although the midfielder was coy on his links with Chelsea.
"I don't want to tell you everything what happened during the transfer," he said to beIN Sport. "This was done at the last minute. In a transfer window, there is always a list of players, you never know if it's true or not. But for me, I knew [Moyes] was interested in me.
"Chelsea? No comment. Arsenal? It's true, they were interested, but Manchester United convinced me to sign for them."
Fellaini went on to hail the impact Moyes has had on his career after bringing him to the Premier League from Standard Liege in 2008 and acknowledges he is frustrated with his early performances for United.
He continued: "David Moyes has given me confidence. When I was in trouble early at Everton, he helped me and supported me. He did everything for me to become a great player. I was criticized, nobody knew who I was. I succeeded because I worked a lot. That's why I'm playing for Manchester United today.
"[I am not trying to] replace [Paul] Scholes or [Michael] Carrick or anyone. I try to play my own game. It is difficult at the moment, but I will succeed."