The 19-year-old was close to signing for the Reds, as they were prepared to pay £8 million and send him back to Fulham for the rest of the season.
However, the BBC reports that time ran out on the transfer on deadline day.
Carvalho could not be loaned back to Fulham in time, as the EFL does not allow deal sheets, and the clubs could not submit the full paperwork before the window shut.
Fulham refused to sell unless they got the youngster back for the rest of this season.
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