According to Sky Italia, Liverpool have had a £45million bid rejected by Juventus ahead of the January transfer window deadline.
Demiral has struggled for game time at Juventus since returning from injury in December.
His only league start in 2021 came in the 3-1 win over Sassuolo and was an unused substitute last time out against Sampdoria.
Giorgio Chiellini, Leonardo Bonucci and Matthijs de Ligt are thought to be ahead of him in the pecking order.
