Pereira spent the second-half of last season on-loan with Fla, helping them to runners-up positions in both the Brasileiro Serie A and the Copa Libertadores.
Globoesporte says Fla want to keep hold of the midfielder and have offered €8m to sign him permanently.
For his part, Brazil international Pereira has admitted hopes of staying with Fla this year.
In 18 games, Pereira scored five goals and produced one assist.
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