According to The Sun, both clubs were expected to meet the Brazilian's agent on June 8 to discuss the possibility of signing the 21-year-old, who scored 12 goals and carved out seven assists for Bordeaux last season.
Malcom has made no secret of his desire to play in the UEFA Champions League, or to move to a bigger club than Bordeaux, while the Ligue 1 side have said that they won't stand in his way when he decides upon his preferred destination.
Both the Reds and Spurs would be able to fulfil the Brazilian's wish to play in Europe's elite club competition - unlike Chelsea, who have reportedly also held talks with Malcom. Arsenal would have faced the same drawback as Chelsea, but have dropped their interest in the Brazilian in any case, according to L'Equipe.
However, despite his outstanding displays in Ligue 1, there may be some concern that Malcom could potentially find it difficult to adapt to the pace and physicality of the Premier League.
He may also struggle to hold down a starting berth - not least at Liverpool, who already have a well-established front three and are reportedly very close to signing France attacking midfielder Nabil Fekir.
In case he decides that the Premier League wouldn't suit him at this stage of his career, both Inter and Paris Saint-Germain - both of whom will be in next season's Champions League - are also potential destinations for Malcom, who told beIN SPORTS: "PSG is the dream too."
Wherever the Brazilian moves this summer, he won't come cheap, being rated at £50m. However, if he continues to develop as impressively as he has at Bordeaux, his potential buyers may consider that a very small price to pay for a player of his evident talents.