The Portuguese youngster fell out of favour under Jurgen Klopp in the second half of last season and was shipped out to Leipzig on a temporary basis for the 2023-24 campaign.
Carvalho has made 14 appearances for Marco Rose's side since arriving in Germany, but he is yet to register a goal or assist and has only made one Bundesliga start for Die Roten Bullen.
Xavi Simons and Christoph Baumgartner are both above Carvalho in the pecking order, although Emil Forsberg's imminent move to New York Red Bulls in January could benefit the 21-year-old's chances of earning more game time.
However, having played a mere 354 minutes for Leipzig so far, Carvalho is being tipped to return to Liverpool in January, and the Reds are apparently discussing an early termination with Leipzig.
Lijnders was asked about the 21-year-old's situation ahead of Wednesday's EFL Cup quarter-final clash with West Ham United, and while he conceded that Carvalho "needs minutes", he revealed that the two clubs had yet to find a solution.
"It's most important he finds rhythm; we all know a player with rhythm is a different player than a player without," Lijnders said at his pre-game press conference. "A player with confidence or without confidence, and a player who trains in a certain way, is a different player.
"He needs to find minutes, but it's not up to me, it's up to our directors to speak with the club and find the best solution for him. We all want the best for him because he is our player, so wait and see, but no decision [has been] made about that."
Carvalho burst onto the scene with Fulham before joining Liverpool on a five-year contract in the summer of 2022, and he ended his debut campaign with three goals from 21 matches in all tournaments.
While Carvalho swapped Anfield for the Red Bull Arena, Dominik Szoboszlai went in the opposite direction during the summer transfer window and immediately adapted to the rigours of the Premier League in Klopp's new-look midfield.
The Hungary international struggled to impress against Manchester United at the weekend, though, as he was taken off after just 61 minutes of that goalless draw at Anfield, and Lijnders has stressed that must "work harder" and "train better" to reach his previous level.
"He is 22. He is so young. We are really happy that he made an impact already. We know what he is capable of. The only way to come back to the standards he has is to work harder, to work better, to train better," Lijnders said of Szoboszlai.
"Rhythm he has, because he plays games constantly. I am not saying that he is not [doing these things], so understand me right there. He has this character that he wants to show, he wants to be important for the team. As long as he keeps that and he fights and the team around him is stable, he will come back to his best as well.
"But we already saw what he is capable of and that's something we need. Last year everybody was saying we need to renew our midfield, we need new boys there. Now we have new boys and for some there will always be difficult phases in a season, more less-top moments in the season. We are just really happy he is with us, that's for sure."
Lijnders also provided the latest on some of Liverpool's injury victims ahead of Wednesday's game, including a positive update on Ryan Gravenberch, but he had bad news to share on Ben Doak's knee injury.