According to reports in Scandinavia, the 24-year-old is set to arrive in Merseyside on Tuesday, with the Reds ready to pip a host of rival Premier League clubs to the Norway international's signature.
Brendan Rodgers has already added Daniel Sturridge to his Anfield ranks this month, and now looks set to sign the highly-rated Forren, as central defensive back-up to first-choice pairing Daniel Agger and Martin Skrtel.
Forren has racked up nearly 150 appearances with boyhood club Molde, and boasts five caps with Drillo Olsen's national team.
Everton and Fulham were both hoping to sign the talented star, who has been tipped for a bright future by Manchester United legend and Molde boss Ole Gunnar Solksjaer.
Forren's prospective arrival at Liverpool will raise further questions over the future of Uruguayan stopper Sebastien Coates, who had been recently linked with a loan move away to gain some more first-team experience.
Speaking to the Daily Mirror, Scandinavian football expert Brendan Husebo said that Liverpool have potentially got their hands on a very talented defender.
"Forren was by far and away the best player in the Norwegian Premier League last year. But what made a big move inevitable was the way he extended that to internationals and the Europa League.
"After looking like lost potential, Forren has become calmness personified under Ole Gunnar Solskjaer.
"A skilful, strong, left-footed centre back might sound familiar to Liverpool fans, and comparisons to Daniel Agger in terms of style and potential are wholly justifiable."