Martinez believes that rumours will surface 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," Soccerway quotes Martinez as saying.
"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 has two years remaining on his current deal at Goodison Park.