The 21-year-old struggled for game time under Jurgen Klopp in the second half of season, often to the chagrin of supporters, and was sent to Germany in the hope of earning regular minutes for the first team.
Leipzig have prided themselves on nurturing young talent down the years, but Carvalho has only been a bit-part player for Marco Rose, managing a mere 12 appearances in all competitions.
The Reds loanee is still waiting for his first goal or assist for Leipzig, and he has started just two of those 12 contests, a Bundesliga clash with Borussia Monchengladbach and DFB-Pokal win over Wehen Wiesbaden in September.
Lois Openda, Christoph Baumgartner and in-form Paris Saint-Germain loanee Xavi Simons are all preferred in the attacking third over Carvalho, who is also behind Emil Forsberg and Benjamin Sesko in the pecking order.
Overall, the former Fulham youngster has only played 257 minutes of competitive football for Die Roten Bullen, although there is hope that he could make just his third start of the season in Wednesday's Champions League clash with BSC Young Boys, as Rose's side are already through to the last 16.
Nevertheless, journalist Fabrizio Romano reports that Liverpool have been left dissatisfied with Carvalho's loan spell in the Bundesliga and have begun discussions to terminate his stay in Germany.
Romano adds that the Reds will soon decide on a course of action with Leipzig, who do not have an option or obligation to make Carvalho's deal permanent at the end of the 2023-24 season.
Carvalho burst onto the scene with Fulham under Marco Silva, playing a pivotal role in the Cottagers'
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