Press Association Sport understands 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 and Belgian side Club Brugge were also linked with a move for the defender. Forren's arrival, albeit on trial, leaves Liverpool defender Sebastian Coates' position in question.
Earlier this month Rodgers admitted the Uruguay international, who has made just nine appearances this season - only two in the Premier League as substitute, could go out on loan if adequate cover could be found.
"It has been difficult for him to get games and the best thing for Sebastian would be to go out and get his games," said the Reds boss.
In November Forren, when asked about a move to England and links with Everton, said: "I cannot stand here and say that I'm not interested - after all the Premier League is involved and Everton are a great club.
"I feel ready. I have had many great matches in the Europa League in the league and the national team.
"I have done well and it tempts me more and more to take the next step.
"I have developed myself a lot this year but right now my focus is on performing well."
- Sports & Recreation