The 21-year-old is seeking a fresh move after a proposed season-long stint at RB Leipzig was ended early due to a lack of playing time.
Carvalho managed just a single Bundesliga start after making the switch to Germany in June.
Unhappy with that situation, Liverpool recalled the youngster earlier this month with the intention of finding a second loan club where minutes could be guaranteed.
However, This Is Anfield understands it is Hull City who have emerged as front-runners in the race for his signature.
They boast a highly rated coach in Liam Rosenior, who has transformed the Humberside club’s fortunes since taking over in November 2022.
Hull were just one point outside the Championship relegation zone upon the Englishman’s appointment, but comfortably avoided relegation and now find themselves in playoff contention this season.
Rosenior has also made good use of another Liverpool loanee this term in Tyler Morton.
The Wirral-born midfielder has made 20 Championship appearances for Hull since joining on a season-long loan, scoring two goals in that time.
Carvalho will hope for similar success should he, as is now expected, make the switch to the MKM Stadium.