Leicester City have become the latest club to join the hunt for Malcom's signature as the race to sign the 21-year-old forward heats up.
Everton have also been taking an interest in the Brazilian, having sent club officials to meet with Bordeaux in an effort to try and negotiate a deal.
However, the latest reports suggest that Roma are leading the chase, with Sky Sports News reporting that a £31.3m offer has been made. Bordeaux are expected to respond within the next 24 to 48 hours.
Malcom's agent Fernando Garcia revealed on Thursday that he had been in contact with Roma's director of football Monchi. Roma are hoping to move quickly as they seek to show their ambition following the sale of Alisson to Liverpool.
"It is a possibility," was all Monchi would say when asked about the possibility of signing Malcom during the unveiling of Patrick Kluivert at the Stadio Olimpico on Thursday.
Everton and Leicester will have to pick up the pace if they are to hijack the move and bring Malcom to the Premier League. L'Equipe claims that Malcom's representatives met with Roma last night to "get things done".
However, Roma's bid is believed to be around £9m short of Bordeaux's valuation, so it might not be a done deal quite yet. Having pocketed £67m from the Alisson deal, making up that difference shouldn't be too much of a problem.
L'Equipe also claims that Valencia are considering whether to join the race. Apparently they were monitoring the situation several weeks ago but have not yet made their interest known with a bid.