The 25-year-old Belgian midfielder joined United on deadline day from Everton in a £27.5million move, the only substantial deal that the Premier League champions managed over the course of the summer.
Despite seeing Arsenal in top form, and some way ahead of United at this stage - Fellaini says he does not regret his decision to move to Old Trafford.
"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 says he could not turn down the chance to work with David Moyes again.
"David Moyes has given me confidence," he said.
"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."
"it's too early for any player to be judged 9 games into the season, especially playing so few games so far"....no it's not. Seriously. It's just not, at all. Read the headlines of this website and any tabloid rag and you'll see how wrong you really are. It's hunting season, and this guys gonna get it big time because of the price you paid for him....unless of course he suddenly transforms himself into a competent and skillful ball player. Fellaini is mediocre at best, and yous have been robbed by Kenwright. You deserve all manner of sustained media abuse for your club's incompetence in buying him AND Moyes so get used to it. If I was Fellaini I would have kept my mouth shut here, it must be embarrassing!!! Especially now Arsenal are officially the best team in the world, ever! Why would they snub him, apparently they only buy people of the quality of Ozil. Man U's incompetence is further highlighted by the contract they handed to Nani. Doh!!! Whats' all that about? Yous are up sh*t creek, and your midfield saviour simply cannot cut it. Unlucky. I don't agree with you though @script....we're STILL riding it out, and have a lot more to prove, but I am much happier in our position than theirs!- red wool