However, reports in his homeland claim that he has been invited to the Reds’ training complex by manager Brendan Rodgers, who is tempted to make an official bid for his signature.
Everton boss David Moyes has scouted the centre-half on two occasions, and is thought to be preparing a move.
Fulham, Manchester United and a number of top European clubs are also said to be monitoring his situation.
He has previously rejected a switch to Belgian giants Club Brugges, claiming that he sees his future in the Premier League, leaving the door open for the Merseyside duo.
There have been some reports that Liverpool had agreed a £4m deal to sign the 24-year-old, however these are believed to be false.
Forren has been impressive in the Norwegian Tippeligaen, helping his current club Molde to the 2012 title under the stewardship of Ole Gunnar Solskjaer.
He has drawn comparisons with current Anfield defender Daniel Agger, due to his solid reading of the game and attacking abilities.