Chelsea have held talks with the representatives of Bordeaux star Malcom over a summer transfer, though they face competition from Liverpool according to Metro.
Manchester United, Arsenal and Tottenham Hotspur made a move to sign the 21-year-old during last January's winter transfer window but his club refused to sell.
French newspaper Sud-Ouest has claimed that the agent of the youngster, Fernando Garcia, has already met with the Blues.
Malcom, an attacking winger, scored 12 goals in 35 Ligue 1 appearances last season.
And in March, he confirmed he was learning English ahead of a move to the English Premier League.
"I have learned the language very quickly, had no big troubles," he said.
"French was much more difficult.
"So I would manage to live in England. But in the end I can integrate everywhere."