The 27-year-old, who joined the Toffees in 2007, has been linked with United after claims on Twitter said the club may submit an offer during the January transfer window.
But the England international, while stressing the importance of realising his Champions League ambition, insists he is set to stay at Everton.
"I'm not that into Twitter but I would say not to be worried," Baines told Sky Sports News.
"There have been a few windows and a few rumours and there's nothing to worry about.
"There are a lot of lads here who have been at the club for a long time now and we want to bring it not just for ourselves and our own ambitions but for the other people at the club, the manager, the chairman, the fans.
"It would be a massive achievement for us if we could get those European nights back at Goodison.
"Although there's a lot of hard work and a lot of other clubs scrapping for that fourth spot, we'd like to think that if we can get our form back on track we could be one of them."