Arsenal reportedly failed in an official approach to sign Malcom from Bordeaux during the January transfer window.
The Gunners were heavily linked with the 20-year-old when the winter window reopened, while the likes of Tottenham Hotspur and Liverpool were also credited with an interest.
Arsenal eventually brought in Henrikh Mkhitaryan and Pierre-Emerick Aubameyang, but German publication Bild reports that they did see a concrete offer rejected for Malcom.
The report claims that Arsenal bid £37.5m for the Brazilian, but Bordeaux were unwilling to sell for anything less than €50m (£44.7m), in addition to a further €10m (£8.9m) in bonuses.
The player has since been linked with German giants Bayern Munich too, with the Bundesliga leaders thought to be in talks to sign him at the end of the season.
Malcom has scored eight goals and created six more in 25 Ligue 1 appearances for Bordeaux this season.
