However, the Reds want €40 million in return.
Atletico see the Serbian international as the ideal replacement for Rodri, who is wanted by Manchester City this summer.
And Liverpool are willing to sell the player who is impressing on loan at Hertha Berlin in Germany.
However, they want a big fee, as they believe Grujic would be able to integrate with the first team next season.
Grujic is only 22 but has been called Hertha's best midfielder in decades after his impressive displays this season.