It emerged earlier this week that Barca were considering a move for the 21 year-old, who had been on the Catalans' radar since his time as a junior with Botafogo.
Globoesporte says Barca have now made an opening bid of €6m for Fernandes.
However, for the moment, Palmeiras are yet to respond. The board are still mulling over whether they can afford to lose Fernandes for the new season.
Should a deal be settled, Fernandes would initially be registered with Javier García Pimienta's Barca B team.