The 19-year-old has just five months remaining on his current deal at Craven Cottage, and will be free to talk to other English clubs in the summer, with a compensation fee then to be decided.
However, according to the Daily Mail, Liverpool are attempting to beat off the summer interest by completing a deal for Carvalho before the January transfer deadline closes on Monday.
The report states how a £5m transfer fee is being discussed between the two clubs, which would then involve the youngster being loaned back to Fulham for the remainder of the 2021-22 campaign.
Fulham boss Marco Silva has continuously reiterated his desire to keep Carvalho at the club this month and beyond, but the club and player have so far been unable to agree terms on a contract extension.
The attacking midfielder has been integral to Fulham's promotion push this season, scoring seven goals and adding four assists to help his side to the summit of the Championship table. body check tags ::