The England full-back says that he knew of no contact from the Red Devils during the summer transfer window and hopes he can fulfil his ambitions at Goodison Park
The left-back was widely reported to be a target for the Red Devils as they searched for a long-term successor for Patrice Evra.
Sir Alex Ferguson eventually turned to Vitesse full-back Alexandre Buttner but Baines says he knew of no contact from the Red Devils.
"People were asking me and yet I didn't know anything," he told reporters. "It was getting mentioned that often that I was getting puzzled by it and yet I'd heard nothing.
"As far as I knew, there was not a great deal in it."
Baines claimed that he was not the type of player to push for a move to a bigger club but did not deny that he had ambitions of winning trophies and playing football on a continental and international stage.
The 27-year-old argued that Everton had proved that they had the ability to win trophies, however, having come close to FA Cup triumphs in previous years.
"I've never been one to rock the boat," he continued. "I appreciate the position I'm in in life and I love what I do. At the same time you do have to have that ambition because it doesn't last long and before you know it it'll be over.
"The ambition for Everton is to finish as high as we can and if we can build on what we've done so far we have a chance of getting back towards European football.
"The main thing in football at club level is the Champions League which is always going to be an aim and if you can do that it strengthens your chances at international level as well.
"That's one of the main ambitions and obviously to win a trophy at some point. We lost in a cup final a few years ago [the 2009 FA Cup final to Chelsea] and lost in a semi-final to Liverpool [in the FA Cup last season] so we know it's not beyond us."
The England international, who is part of the Three Lions squad for the upcoming World Cup 2014 qualifiers, was encouraged by the way that the Toffees had not only added to their squad this summer but retained their key players.
"Over the last few seasons, we've tended to lose one of our assets each summer, whether it be Joleon [Lescott], Mikel Arteta when he left, Steven Pienaar,'' he explained.
"This season we've not only managed to keep the squad together but added really good players."