The 21-year-old Brazilian winger is seen as one of the biggest prospects on the continent.
Inter attempted to sign him for £35 million, but their bid was knocked back.
RMC Sport suggests the offer was not what Bordeaux are hoping to get for Malcom.
Inter wanted to pay the fee in installments, while Bordeaux want all the money now so they can invest it in their squad.
It will be up to Arsenal or Tottenham to make an offer high enough to convince the French side to sell their prized asset.