Martinez is also bemused by reports the Argentinian, who is reportedly valued at £4million after scoring 19 goals for the Championship side this season, watched Latics' FA Cup third-round replay win at Bournemouth on Tuesday.
Those rumours circulated as Becchio, 29, missed Leeds' match at Birmingham on the same night through illness.
When asked about those suggestions, Martinez said: "I don't think so. If he was I didn't know about it."
Wigan have already made two signings in the current transfer window by bringing in Honduras international Roger Espinoza on a permanent deal and Chilean striker Angelo Henriquez on loan from Manchester United.
A season-ending injury to defender Ivan Ramis has increased the possibility of further business but Martinez, facing up to another Barclays Premier League relegation battle, does not want to make his intentions public.
When asked specifically about Becchio at a press conference, Martinez said: "I am not going to mention any names.
"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.
"We are looking for the right player, somebody that can help us. But the focus is on the players we already have here.
"They have the experience of what is needed at Wigan Athletic - the way we need to play, what we need to achieve. 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."