The Reds have been strongly linked with a move for the Danish midfielder.
Hodgson is keen to bring in Poulsen as a replacement for Javier Mascherano, who is closing in on a move to Inter Milan.
“If we can sign him from Juventus at a price I consider reasonable, he will be a very good player to bring into our team,” Hodgson told Ekstra Bladet.
“Christian is a player I know well, a player whose career I actually kick-started many years ago and I have followed him closely ever since.”
