The Bundesliga team are ready to secure the Portuguese on a permanent basis.
Per The Times, Leipzig made an attempt to free Carvalho from his current Liverpool struggles in the summer.
They made a permanent offer for the 20-year-old, which Liverpool appear to have turned down.
The Reds still believe that Carvalho can play a role for the first team in the coming years.
However, the former Fulham star wants to play regularly or prefers a move away from the club.