Goal understands the 20-year-old has been earmarked as a replacement for Alexis Sanchez following his impressive performances in Ligue 1 this season.
Malcom has scored seven goals and laid on five more for his team-mates in the French top-flight in 2017-18, with Manchester United and Tottenham having also shown an interest in bringing him to the Premier League.
Raul Sanllehi, Arsenal’s new head of football operations, has been heavily involved in the negotiations despite not formally starting his role at the club until February 1.
Gunners boss Arsene Wenger refused to deny his interest in the Brazilian after Arsenal’s defeat at Bournemouth, but said there was "nothing concrete" and that "it’s better he didn’t come out on any specific name".
Wenger is also open to the idea of accepting a player swap deal from Manchester United for Alexis, with Henrikh Mkhitaryan mooted as one of several options.
However, it’s understood that Manchester City remain in the race to sign Alexis with the Chile international yet to make a decision on which team he will sign for this month.
*Additional reporting from Chris Wheatley