The Times says the highly-rated 19-year-old looked set to switch Craven Cottage for Anfield on deadline day, with Neco Williams moving in the opposite direction on a temporary basis until the end of the season.
However, while Williams did get his move to Fulham, Carvalho's transfer to Liverpool ended up falling through at the last minute.
A fee had been agreed between the two clubs, but the necessary paperwork was not completed in time, meaning that the youngster remains at Fulham for now.
The creative midfielder is out of contract at Fulham in June, but Liverpool would have to pay the west London club a compensation fee if they do decide to pursue Carvalho.
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