That is according to club president Stephane Martin.
The Brazilian has been heavily linked with a move to Arsenal in recent weeks, as the club prepare for the departure of Alexis Sanchez.
While Pierre-Emerick Aubameyang and Thomas Lemar have also been touted as replacements for the Chilean, a deal for Malcom looked most likely when the player's agent was spotted in London last week.
But Martin has poured cold water on the speculation.
“Things are clear with his agents,” he told French media outlet L'Equipe.
How Arsenal could line up if Malcom and Pierre-Emerick Aubameyang sign
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“They can always try, but they will have a hard time taking him from us”
Stephane Martin
“We did not sign him to an extension and tie him to something, to let him go this winter.
"We have 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."
Getty
Getty
Malcom extended his contract at the Ligue 1 side at the start of the season.
The 20-year-old has impressed after joining Bordeaux from Brazilian outfit Corinthians.
Arsenal are also hopeful of completing a deal for Manchester United winger Henrikh Mkhitaryan in the coming days.