Reds manager and former Dortmund boss Jurgen Klopp has outlined this summer his admiration of the USA international.
With Nabil Fekir's £53m transfer from Lyon having collapsed, Pulisic is seen as another option.
However, the Liverpool Echo say Klopp is not prepared to spend £60m/£70m on a squad player this summer.
It is believed Pulisic would not break into Liverpool's strong starting XI just yet.
But the club and Klopp are keen and it is expected a fresh move will be made for the Bundesliga talent in 2019.