The Latics boss also denied suggestions that Becchio, who has scored 19 goals this season for the Championship club, watched Athletic's FA Cup third-round replay win at Bournemouth on Tuesday.
These rumours emerged after the 29-year-old player missed Leeds' own Cup replay at Birmingham on the same night because of illness.
When asked if Becchio had been at Dean Court, Martinez said: "I don't think so. If he was I didn't know about it."
When questioned if Becchio was one of his targets during the January transfer window, Martinez replied: "I am not going to mention any names.
"We are looking for the right player, somebody that can help us. But the focus is on the players we already have here.
"I will never go into a position of mentioning names of other players that are involved with other football clubs. I don't think it is respectful. I don't like it when people do it about our players in the middle of a season and I would never do that."
Martinez did admit that Wigan, who have already signed Honduras international midfielder or defender Roger Espinoza and Chilean striker Angelo Henriquez on loan from Manchester United this window, are in the market for more additions, particularly after losing defender Ivan Ramis for the remainder of the season through injury.
"We have got a little bit of room to bring one or two players. I spoke with the chairman yesterday and the injury to Ivan has put us in that situation," added Martinez.