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The north London rivals have both been heavily linked with the Brazilian throughout the January transfer window.
Arsenal are desperate for reinforcements in attack as they look to replace Alexis Sanchez, who is set to join Manchester United this week.
Armenian winger Henrikh Mkhitaryan will be joining the Gunners in a swap deal but boss Arsene Wenger wants more fresh faces.
Spurs are keen to add the 20-year-old to their exciting project and Malcom’s representatives have reportedly been impressed with Mauricio Pochettino’s vision for developing young players at the club.
How Arsenal could line up if Malcom and Pierre-Emerick Aubameyang sign

“Is England a dream? Yes it is a dream, it is a dream for all players and I am no different.”
Bordeaux winger Malcom
Liverpool have also been touted as a potential destination as Jurgen Klopp looks to fill the void left by the sale of Philippe Coutinho to Barcelona.
The clubs could be set to battle to sign the former Corinthians ace and they’ll have been put on red alert by his latest comments.
Following Bordeaux’s 1-0 win over Nantes yesterday he said: “I do not know if I will be staying or leaving.
“I leave that to my agents, to the club. If I leave that is great, I thank the club for everything.
"That is life. These are choices. There you go. Now we will see. If I have to stay, I will stay. If I am to leave, then I will leave. So long as I am here, I will do my work.
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"Is England a dream? Yes it is a dream, it is a dream for all players and I am no different. As I said, I am here, I must think about working and nothing else. I must not think about leaving now.”
Malcom has been in stunning form for the Ligue 1 side so far this season, scoring seven times and providing six assists.
All three Premier League sides will be keen to add him to their ranks as they look to qualify for next season’s Champions League.
Just two points separates the north London enemies in the table, with fifth-placed Tottenham sitting one place above their rivals.
Liverpool are fourth, six points behind second-placed Manchester United.