Jurgen Klopp's side won the race to sign the Portuguese protege from Fulham last summer, and he made an immediate impact in the Reds' first team.
Carvalho scored in back-to-back games against Bournemouth and Newcastle United in the first few weeks of the season, netting a 98th-minute winner against the latter in a 2-1 success.
However, the 20-year-old soon found first-team opportunities hard to come by, and he played a paltry eight minutes of Premier League football following the World Cup.
Klopp has sympathised with Carvalho's situation, and the Portugal Under-21 international has been tipped to leave either on loan or permanently this summer in search of regular game time.
Leipzig are thought to have previously tabled at least two bids for the former Fulham man, but Liverpool are against the idea of a permanent exit at this moment in time.
West Ham United are also said to have made a loan offer for the versatile attacker - who has also been deployed in the engine room - but according to Fabrizio Romano, Leipzig have now reached an agreement for the temporary signing of Carvalho.
Romano claims that Carvalho is set to join Die Roten Bullen on loan for the 2023-24 campaign, and the two clubs plan to thrash out the final details next week before his move is made official.
Leipzig will reportedly not have the option to make Carvalho's deal permanent at the end of the campaign, as Liverpool chiefs still believe that the 20-year-old can become an important part of the Reds' first-team plans.
Having also netted in an EFL Cup fourth-round defeat to Manchester City, Carvalho ended his debut season at Liverpool with three goals from 22 matches in all tournaments, but he played just 340 minutes of Premier League football in total.
The former England youth international came off the bench for the final minute of Liverpool's Community Shield triumph over Manchester City in his competitive debut, while he played the full 90 minutes in their 7-1 Champions League group-stage drubbing of Rangers.
Carvalho is set to become the third Liverpool player to leave the club on loan this summer, following the temporary exits of right-back Calvin Ramsay and goalkeeper Harvey Davies to Preston North End and Crewe Alexandra respectively.
Several of Carvalho's fellow midfielders have left Liverpool permanently ahead of the 2023-24 season, including Naby Keita, Alex Oxlade-Chamberlain, Leighton Clarkson, James Milner and Juventus loanee Arthur, as well as Roberto Firmino.
The Reds have already welcomed Alexis Mac Allister to the club in a £35m deal from Brighton & Hove Albion and are believed to be working on a move for Nice's Khephren Thuram, as Klopp aims to bring at least three new midfielders to Anfield in the current transfer window.