Malcom was heavily linked with a move to the Premier League in January, with the likes of Manchester United, Liverpool and Arsenal all credited with an interest.
A number of Europe's top clubs including Paris Saint-Germain and Bayern Munich were also thought to be monitoring his situation, but Malcom instead decided to stay in France until at least the end of the season.
Interest in the 21-year-old has subsided for most clubs previously thought to be in the race, but The Mirror reports that Spurs remain very interested in the forward.
Talks are understood to be well underway between the two clubs as they look to come to an agreement over a fee for the Brazilian before the end of the transfer window on August 9.
However, Spurs could face competition for his signature from Inter Milan, who have also been keeping tabs on the player.