The Daily Mail says Mendes, whose client list is headed by Cristiano Ronaldo and brokered the move that took Ruben Dias to Manchester City, sees Carvalho as a potential star of the future.
The teenage midfield creator is in the final year of his contract at Craven Cottage having scored four goals in 12 games for Marco Silva's team.
Mendes has alerted Barcelona and Real Madrid without joy but believes Liverpool are more interested in the 19-year-old having signed another Fulham academy graduate Harvey Elliott with great success.
Mendes has good relationships with the Anfield club having been involved in Diogo Jota's move there from Wolves.
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