With Bilbao almost certain of a top-four finish in La Liga this season, it had been reported that the club would make a move for Martinez when the transfer window opens.
However, the Spanish international, who has also been linked with Barcelona, doubts that Bilbao would offer in the region of £25m for his services.
"There's nothing in it," Inside Spanish Football quotes Martinez saying.
"I don't think Athletic are going to come here offering €30m (£25m) to their enemies at all. On top of that, I'd never head over to the other side, so the fans can be calm that'll never happen."
Martinez, 22, came through the youth system at Sociedad.