Jakob Friis-Hansen, the Reds' scout in the area, has revealed that boss Rafael Benitez is keen on Jorgensen.
"I have previously advised Liverpool over two Danes, with Daniel Agger and Nicola Savic, both of whom they purchased and are almost too happy with," said Friis-Hansen to Sporten.dk.
"I gave them Mathias Jorgensen's name a long time ago and Liverpool are wild about him. They are keeping very good track of him.
"Liverpool see him as a very promising youngster, like I do, and clearly just like a player who will play for the Danish national team for many years to come."