Valentin Hobel, the Austria international's agent, expects his client to be charged with filling the void in defensive midfield left by Javier Mascherano's impending departure if negotiations are successful.
"Hodgson thinks that Paul's strengths in midfield are better than his attributes in central defence."
Premier League rivals Aston Villa and Sunderland remain interested in the colourful centre-back but Hobel revealed that Scharner, who can also play in midfield, would relish a dream move to Merseyside.
He added: "Liverpool would be a dream, of course, but we are in contact with several clubs. Because he is a free transfer, he can choose."