Barcelona president Josep Maria Bartomeu has transfer-listed Malcom ahead of the summer market kicking off.
The Brazilian winger only moved to Barca last August from Bordeaux, but has struggled for form and fitness over the past season.
Sport says Bartomeu is now ready to sell the winger.
Several Premier League clubs have expressed interest in Malcom, with Everton and Tottenham heading the queue.
Bartomeu will seek to sell for at least the €41m they paid Bordeaux for Malcom at the beginning of last season.