Mundo Deportivo says the player is willing to stay at Barca next season, despite his limited game time.
However, the club are apparently willing to consider the Brazilian's sale should they receive an acceptable offer.
Arsenal were linked with a loan move for the winger during the 2018/19 season but nothing came to pass.
The report claims Barca are aware of interest from both the Gunners and their London rivals, Tottenham.
Unai Emery's side cannot offer Champions League football but Malcom would probably see more action at the Emirates.