Goal exclusively revealed in June that Arsene Wenger was plotting a £22 million bid for the former Everton man, but were only willing to offer a £70,000-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.
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"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 admits 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 criticised, 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 Scholes or Carrick or anyone. I try to play my own game. It is difficult at the moment, but I will succeed."