The 28-year-old defender was strongly linked with joining former Everton manager David Moyes at Manchester United in the most recent transfer window.
However, a deal never materialised and Baines has started this season strongly, scoring twice for Everton and featuring in England's final two FIFA World Cup qualifiers.
Martinez believes speculation is simply par for the course when a player is performing well for club and country.
"As a manager, the only thing that concerns me is to see Leighton enjoying his football and being consistent with his performances," he said.
"You're not going to stop the rumours and the talk; that comes with a player performing so well. You are always going to get that.
"So I'm not concerned about that. All I want is Leighton to be proud of being an Everton footballer, carry on enjoying his football and carry on performing in the manner that he's been doing. That's the only thing I want."
Baines is into the final two years of his contract at Goodison Park, but Martinez does not believe a new deal would stop rumours about his future.
"I don't think there will be any less speculation if he signs a new contract," Baines said.
"Leighton is an icon for us. He's not just a top left-back, he's an Evertonian and an icon of the club. It is about what he represents to us so signing a contract or not.
"Edison Cavani signed a contract (for Napoli) and was sold (to Paris Saint-Germain). Throughout the world of football, footballers have become big assets and that's not going to change."
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