Yet Martinez, whose side visit champions Chelsea in the Premier League on Saturday, said the move was only at an early stage.
"There has been an initial approach, but there is a long gap until official confirmation," Martinez told reporters on Friday.
"If there's a signing to be made, it needs to be the right character, the right addition. In any process there are steps. Some become very long, others are quite short."
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Striker Steven Naismith looks set to leave Goodison Park during the January transfer window.
Swansea City boss Alan Curtis has confirmed his interest in signing the Scotland international, who has played just once in the Premier League since mid-October.
Martinez, however, said another Premier League club, reported to be Norwich City, were on the verge of agreeing a deal for the player.
"No, there is no agreement with Swansea. Obviously there's been another Premier League club we made a lot of progress with in that respect," Martinez said.
"I would say everything is more or less agreed in terms of a transfer. We spoke to another Premier League club, and that deal has been there since Jan. 1. But it's about sitting down with the player."
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Toby Davis)
