The 28-year-old, signed from Tromso six years ago, is in advanced talks with the Ewood Park club.
Manager Sam Allardyce said: "Morten has a deal on the table and his representatives will be over, no doubt, to finalise that deal with the chairman in the next few days or weeks.
"We certainly hope he does agree terms and signs on for the next few years."
Rovers have secured the services of promising Canadian youngster Junior Hoilett on a two-and-a-half year contract. The 19-year-old, who was first taken on trial by the club at the age of 12, has made a big impression after breaking into the first team this season.
Allardyce added: "It is one of the hardest and longest negotiations I have experienced but finally we have persuaded Junior that Blackburn is the place for him.
"We're really looking forward to his future at Blackburn and hopefully seeing him develop into a fine player."
Meanwhile, Rovers have received a positive update on the fitness of captain Ryan Nelsen.
It was feared the New Zealand international defender could miss the rest of the season after suffering a knee injury in last week's Barclays Premier League defeat of Bolton.
But Allardyce said: "I think he was worried about the injury when it happened, we all were, but now we have had the scan and it has settled down, it only looks a few weeks rather months."
Liverpool v Blackburn. Click here to bet.