Baines was heavily linked with a move to Old Trafford before the start of last season when former Toffees manager David Moyes made an albeit brief switch to Manchester.
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"What the club has done lately is retain its best players," he told the Liverpool Echo.
"Everyone here who has been linked with someone has stayed and committed to the club. The younger lads; Ross [Barkley], [John] Stonesy, Seamus [Coleman] have all been linked with clubs and they've all got their best football ahead of them, but they're all happy to do it here.
"That's as big as anything for me.
"The manager was telling me that's what he wanted to do when I signed my contract.
"I signed following that summer of the whole United thing, but that was in their minds back then in terms of how to change the status and perception so we can keep hold of players when other clubs come calling.
"Since that with me, a few of the other lads have been talked about as going by the media but in all fairness none of them have been the slightest bit interested in playing anywhere else.
"You hear that from them. They are enjoying it here and they want to achieve what they can here."
Baines also says he will be ready for the start of the Premier League, despite only having a short close-season break.
The 29-year-old was part of the England squad that turned in a disappointing World Cup performance, finishing bottom of a group that also contained Costa Rica, Italy and Uruguay.
Baines has not allowed himself too much time to rest since returning from Brazil, but insists the work he has put in over recent weeks will pay off during the coming season.
"I feel alright. Time-wise I didn't have that long off so I had a little rest but I was in sporadically over the summer anyway because I didn't want to de-condition too much.
"I was making sure I got a rest but kept ticking over as well.
"It's the mental as much as the physical sometimes. Being able to switch off and get away is important but I wanted to be ready to hit the ground running."
Everton begin their Premier League campaign at newly promoted Leicester City next Saturday.