The two clubs agreed a package totalling £8 million including add-ons late on Monday but failed to complete the necessary paperwork before the deadline passed.
Although Carvalho cannot be registered as a Liverpool player until the end of the season, talks are continuing, and sources have told ESPN that Liverpool still believe a compromise can be reached, although his valuation remains a sticking point.
The midfielder is out of contract at the end of the season and has rejected at least one offer to sign an extension.
FA rules dictate that Fulham are entitled to receive compensation if he leaves the club on a free transfer, having developed the 19-year-old for seven years.
That figure would be set at just £500,000 if he went to a club outside England but higher should he move to Liverpool or another Premier League side with the exact payment determined by a tribunal.
As part of the original deal, Carvalho would have been loaned back to Fulham for the rest of the season so the Championship club would not be weakened in their attempts to secure promotion to the Premier League.
In that regard, his immediate situation has not changed but the longer his future remains unresolved, the more there is a risk either his move will be decided by a tribunal or another club could scupper Liverpool's plans.