The former Fulham starlet was a regular performer for Jurgen Klopp in the first half of his debut 2022-23 campaign, but he found game time increasingly hard to come by in the second half of the season.
A significant summer of midfield change for Liverpool saw all of Fabinho, Naby Keita, Jordan Henderson, Alex Oxlade-Chamberlain and Leighton Clarkson wave goodbye, while Arthur's disappointing loan spell from Juventus also came to an end.
Nevertheless, Carvalho was given the green light to further his development with Leipzig, who have established a reputation as a club willing to offer consistent minutes to young players.
However, the 21-year-old was only a bit-part player in the Bundesliga under Marco Rose, who preferred Xavi Simons and Christoph Baumgartner in the offensive positions behind Lois Openda.
Carvalho made 15 appearances for Leipzig in all competitions, but he only started three of those matches and failed to register a single goal or assist during his time in Germany.
Carvalho earned just one start in the Bundesliga, one in the Champions League and one in the DFB-Pokal, and it was reported earlier this month that Liverpool were in talks to terminate his loan agreement.
Leipzig did not have an option or obligation to make the 21-year-old's stay permanent, and Liverpool have now announced that the German giants have sent Carvalho back to Anfield for the second portion of the campaign.
It remains to be seen whether Carvalho stays with Liverpool for the rest of the season or if he is sent out on loan again, but he is still believed to be of interest to Premier League teams despite his underwhelming spell with Die Roten Bullen.
After an eight-year spell with Fulham, Carvalho joined Liverpool for a fee of £5.1m in the 2022 summer transfer window and came up with three goals in 21 matches during his first season at the club.
Carvalho made the first XI on four occasions in the 2022-23 Premier League season, and the former Portugal Under-21 international is contracted to Liverpool until the summer of 2027.
Liverpool can move five points clear of Aston Villa at the top of the Premier League table when they open 2024 with a home clash against Newcastle United on Monday evening.