Initial reports yesterday suggested Forren was due at Melwood on Tuesday to undergo a medical, but later in the evening it was reported by several outlets that he was instead beginning a trial at Liverpool and that no bid had been submitted by the club.
That trial now appears to be have been shelved after Southampton agreed a fee with his club, Molde.
The Echo report that the 24 year old was not high on manager Brendan Rodgers’ list of priorities.
Molde boss Ole Gunnar Solskjaer said: “We have had a good dialogue with Liverpool manager Brendan Rodgers, who wanted to speak with Vegard and see him in training.
“We agreed that he could go there to see the conditions. But Liverpool have not made a bid.”
Forren was pictured arriving at Manchester airport on Monday night but is now reported to be heading to the South Coast to undergo a medical and agree personal terms ahead of a £4m move to Southampton.
Liverpool have also been linked with Valenciennes centre-back Nicolas Isimat-Mirin, Reading’s Alex Pearce, and Feyenoord’s Stefan de Vrij.