It is understood the 24-year-old will be at the club's Melwood training ground on Tuesday for manager Brendan Rodgers to begin his assessment of the Molde centre-back.
Reports in Norway had claimed the Reds had a £4million bid accepted and Forren was scheduled to have a medical on Tuesday, but that is not the case.
Forren, who made his competitive international debut in October, was scouted in person at least twice by Everton manager David Moyes recently.
Fulham, Manchester United and Belgian side Club Brugge were also linked with a move for the defender.
Current club Molde FK had agreed terms with Bruges earlier this month, but the stopper was not interested to move to Belgium.
Forren recently revealed that he wants to join a club in the Premier League, otherwise he would "most probably stay in Molde."