Tottenham Hotspur and Arsenal are both keen on Brazilian.
The Brazilian winger is one of the world's most in demand young players after a superb debut season in Europe.
Despite signing Lucas Moura, Tottenham continue to be linked with Malcom, with Le10Sport reporting they will make a fresh approach for the Bordeaux winger this summer, with Arsenal also interested.
PSG though could turn out to be fearsome rivals for his signature.
France Football report PSG sporting director Antero Henrique is keen to avoid missing out on him having identified him as a top talent, as they did with N'Golo Kante and Ousmane Dembele.
Bordeaux are claimed to be looking for up to 50 million Euros (£44 million).
21-year-old Malcom has scored nine goals this season and provided six assists in Ligue 1, netting the winner against Guingamp this weekend.
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