Malcom is desperate to leave Barcelona in the summer after a difficult campaign.
The forward only moved to the Nou Camp last year but has struggled for first team football and Barcelona are willing to let him go if they can recoup the €40million (£39m) they spent on him.
Roma thought they had won the race to sign him from Bordeaux until Barcelona made a late swoop to sign him, although Ernesto Valverde made it clear he had not pushed for the deal.
The Barcelona manager referred to Malcom as a 'signing made by the club'.
That outlook has been made clear as he has only made 19 appearances all season, with Barcelona fighting on three fronts, and been handed eight starts in all competitions.
Now, according to ESPN FC, he wants to leave the Spanish giants in the summer transfer window.
The 21-year-old spent most of the season fighting for his first-team place but in the report it suggests he has now grown frustrated at the lack of chances.
And if a team offers an amount close to the figure Barcelona paid, they will let him leave.
'He is a good footballer and has a good reputation,' a Barcelona source told ESPN FC. 'He's had the option to leave now for a while and we have to respect his decision. But Barca aren't going to give him away.'
His agents are now working to secure him a move elsewhere in Europe. Roma, Inter and AC Milan have previously shown an interest.
Everton, Tottenham and Arsenal were also credited with an interest in the summer.