It has been claimed Arsenal have agreed a €50million move for Brazilian forward Malcom, who signed a four-year renewal in September and has scored seven goals in Ligue 1 this season.
The Gunners are believed to be keen to bolster their attacking options with Alexis Sanchez seemingly set to depart this month or when his contract expires at the end of the campaign.
Martin says Bordeaux have not had any contact with Arsenal about Malcom and he does not anticipate an agreement being reached in the transfer window.
"Things are clear with his agents. He has not had his contract extended this summer just to give him away this winter," Martin told L'Equipe.
"We haven't had any discussions with Arsenal. From our point of view, it's all hot air.
"They can always try, but they will have a hard time taking him from us."