The England international duo have been linked with moves to reigning Premier League champions Manchester United, with David Moyes' men reported to have targeted a £50 million move for midfielder Barkley.
United's interest in full-back Baines looks to have been resurrected from the close-season, with Moyes rumoured to be keen on a reunion with the pair having managed them during his time at Everton.
However, when pressed about potential interest in the duo, Martinez was adamant that they will be going nowhere.
"Speculation doesn't bother me, not when we are in a strong position financially," Martinez said. "As a football club, when you are in a position where you have to bring money in, it can be a really difficult position.
"You can be anxious and frustrated. When you need to make financial decisions, the squad is not going to benefit from it. When you can make football decisions, you're in a strong position. I have no doubt (we can resist bids).
"In football, you can't fight the trend of the game. But what you can dictate is the timing and everything you do should be for the good of the club. We've done it before."
With stability on and off the pitch, on-loan striker Romelu Lukaku said recently that he believes Everton are outsiders for the title, with Martinez's side lying just five points adrift of leaders Arsenal heading into the new year.
The Everton boss, though, is keen to stress the importance of his side continuing their consistent first half of the season, and he believes his team have yet to reach their full potential.
He added: "We're halfway through the season. It's a moment where everyone will assess the season. It's a good landmark - after 19 games we have two defeats, we've been consistent.
"We've got points against the top sides, it's been a really good first half of the season, we're fourth in the table. The 37 points we have is not (a result of) overachieving or being fortunate, it's the opposite. Some of the draws we've had we felt we deserved more.
"I don't think we've fulfilled the potential. The group is excited, we want to push ourselves to get more points in the second half of the season."
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