Indeed, the 29-year-old signed a new four-and-a-half-year contract at Goodison Park just this week and, for the first time in a long time, the decision to stay with the Toffees can be considered an ambitious one.
Everton boss Martinez certainly thinks so, with his side just a point off fourth spot ahead of their clash with Liverpool on Tuesday night - and six above United.
In sum, the 40-year-old believes Baines might just have a better chance of qualifying for Europe's elite competition on Merseyside than under the wing of former manager David Moyes.
"I feel Leighton understands that, as a club, we're ready to kick on and challenge for big things," the Spaniard told reporters.
"As a manager, you want players who want to play Champions League. We don't just want a group of players who are happy to play in the league so for Leighton to commit himself to Everton and give us the best years of his career is very significant in that respect.
"It's a massive boost to the fans but internally it's even more important because everyone who wants to play with Leighton knows we're all going to need to step up to try to achieve the targets that other clubs could offer him.
"You look at the points tally and it'll give you a clear indication that we're not far off and that makes it something worth committing to."
As much as ambition, though, Martinez believes Baines is keen to demonstrate his utmost loyalty to a club that has offered him all it support over the years - something he feels there is less and less of in the modern game.
"I think Leighton is a very intelligent man but he's also an old-fashioned footballer who wants to be loyal," the Everton boss continued. "He doesn't get moved around by the new trend in football.
"He wants to be the best he can and play in the best competitions but, if he can do that with Everton, he feels a lot stronger and those values are needed in the game. They are certainly very important to us."
Was Baines right to snub United and stay at Everton?
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