The French outfit bought the forward from Corinthians for £9m on the final day of the last January transfer window, but they have now set a €50m (£44m) price tag on his head following his electric performances.
The 20-year-old has been a shining light for the Ligue 1 side this season, with seven goals and five assists accrued in his 20 games across competitions so far.
Unsurprisingly, this has lead to a lot of attention from the biggest clubs in Europe, with Goal Brazil reporting Arsenal's recent arrival into the race, alongside fellow English giants Manchester United and Tottenham, as well as Bayern Munich.
It is thought the Manchester club were initally put off by Bordeaux's high asking price, but Jose Mourinho is purportedly desperate to enhance his side's creativy, following some turgid displays over the festive period.
It is therefore likely United will put a bid in over the next month, although their hesitance has allowed Arsenal to get a march on them in terms of negotiations, with talks occurring over the last 10 days.
Arsenal Ace Héctor Bellerín Weighs in on Rumours of Feud Between Alexis Sánchez & Laurent Koscielny @ https://t.co/3CgQPuaozY— ArsenalPro (@ArsenalPro) December 30, 2017
While a new attacking midfielder may not be the most refreshing sight for Gunners' supporters, as with all links to attack minded players, Malcom is seen as a suitable replacement for contract rebel Alexis Sanchez.
In a saga that has failed to subside, Wenger is now supposedly willing to let the Chilean leave in January if a club meets their £35m evaluation, freeing up the necessary funds to acquire the French side's starlet.
Despite Bordeaux's preference for the Brazilian international to stay until the summer, by which time he would presumably have earned a higher price tag in their estimations, it is thought they will not block the youngster's move, should he push for it and their evaluation is met.