The former Wigan boss says both the left-back and team-mate Marouane Fellaini have behaved professionally despite serious interest from David Moyes at Manchester United
Rumours circulated on Wednesday evening that the left-back had requested a transfer in order to force through a move to Old Trafford, where he would join up with former boss David Moyes.
But Martinez, speaking to reporters after the Toffees' 2-1 win over Stevenage in the Capital One Cup, stressed that neither Baines or fellow United target Marouane Fellaini have made any such demands.
"No. You are going to get so many stories. The two players have been true professionals and that is what I want, players that are dedicated to the club and dedicated to the team," he said.
"I am not going to entertain any rumours or speculation. At the moment I really feel for the game. We are concentrating on rumours too much. There is nothing to tell. If there is anything to tell, we will tell our fans straight away."
Fellaini came off the bench to grab an injury-time winner against Stevenage on Wednesday, and Martinez has hailed the Belgian's ability to turn a match on its head.
"What I love about Marouane is his understanding of the game," he added. "He got involved in the creative part of our game and he is someone with a real threat in the final third. When he gets into the final third, he puts real fear in the opposition. He gave us that cutting edge we had been missing."