Arsenal has been linked to the 20-year-old since the January window opened, with reports suggesting Malcom could fill the void potentially left by Alexis Sanchez, who appears to be on the verge of leaving the north London club.
Despite the Premier League side reportedly submitting a bid in excess of £40 million, Martin revealed there has been no contact, claiming Bordeaux is reluctant to part ways with Malcom after extending his stay until 2021 last summer.
"We never had a discussion with Arsenal. From our point of view, it's wind. They can always try, but they will have a hard time taking him from us."
Martin's insistence that Malcom will remain with Bordeaux beyond the January signing period somewhat contradicts recent comments from manager Jocelyn Gourvennec, who revealed the Brazilian is pondering a move to England.
"He isn't unsettled but he is thinking it over," Gourvennec said Monday.
Malcom is one of three players who Arsenal seems to be targeting this month following reports that the Gunners will attempt to include Manchester United midfielder Henrikh Mkhitaryan in the deal for Sanchez. The club is also reportedly confident of signing forward Pierre-Emerick Aubameyang from Borussia Dortmund.