The Reds are already planning ahead for the summer, with manager Jurgen Klopp expected to be busy in the coming transfer window.
They have already had scouts watching the Bundesliga before his arrival at the club, with eyes reportedly on Hoffenheim’s Kevin Volland.
However, if he isn’t available then they have identified Kostic as a potential alternative according to Bild.
The Serbian international is thought to be among the top targets at Anfield, with his direct running, pace and ability on the ball and ideal fit for the football he wants his side to play.
There is however, a complication that could see any move to the Premier League put on hold.
As Serbia are rated 50th in the FIFA rankings, he needs to have played 75% of his nation’s fixtures in the last two years to be eligible for a work permit, something that Kostic has not managed.
However, exceptions are made for special talents and Liverpool would surely apply for that should they make their move for Kostic.