The 19-year-old came close to joining the Reds in January.
Sky Sports states that Carvalho will move to Anfield this summer after Liverpool agreed to pay £5m, which could rise up to £8m with add-ons.
Carvalho's current deal expires this summer and Fulham would be entitled to compensation set by a tribunal
It is believed Carvalho will not be loaned back to Fulham for next season.
Carvalho has scored seven goals in 29 Championship appearances for Marco Silva's side this season
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