Ora Bolas says the Gunners made an approach for the tricky wing ace just before Christmas.
Bordeaux want £44m for the 20-year-old.
The Brazil Under-23 international is contracted to the Ligue 1 club until 2021, but does not have a release clause in his contract.
The report claims that Malcom has a gentleman's agreement with the club that they will allow him to leave next summer.
In France, it's claimed both United and Tottenham have already had offers for Malcom turned down by Bordeaux in the past week.