Fulham are also reportedly interested in bringing back their academy product, whom Liverpool signed from the Cottagers in the summer of 2022.
Interest also comes from the Championship, with the Mail reporting that Leeds, Southampton and Hull City are all keen to bring in the 21-year-old.
Carvalho looked set to spend the season at Champions League outfit RB Leipzig after signing on a season-long loan in the summer - but his spell in Germany quickly turned sour.
While making 15 appearances, only one of those would be as a Bundesliga starter - and in just 135 minutes for the club, he registered no goals or assists.
After his ill-fated spell in Leipzig, Liverpool now need to decide what they want. Carvalho would be guaranteed to play every single week in the Championship - and likely perform as one of the best players in the league.
The Premier League wouldn't give him the same guarantee, though it would give him a much better learning experience. After all, Carvalho has already reached the top of the Championship - it's debatable how much he gains from doing it again.
At the end of the day, game time is what will be the deciding factor on a loan move this month. As things stand, Jurgen Klopp doesn't see much use for Carvalho in his current squad, and the only way that changes is if he proves himself as a top talent.
The potential is obviously there - Carvalho simply needs the chance to extract it.