Liverpool are the latest club to emerge as suitors for Malcom, according to the Mail, with Jurgen Klopp keen to strengthen his attack this summer.
The 21-year-old Brazilian would cost in the region of £40 million and appears set to leave Bordeaux following interest in January.
Tottenham, Manchester United and Arsenal are also keen, but the Reds have Malcom near the top of their list of targets.
Bayer Leverkusen's Leon Bailey and Christian Pulisic of Borussia Dortmund are also under consideration as Klopp aims to spend the £142m received in January from Barcelona for Philippe Coutinho.