The Norway international is out of contract at the end of the season and has been made an offer to stay by Blackburn, whom the 28-year-old joined in 2004.
Allardyce, who expects a decision from the player next week, said: "We have gone as far as we can from a financial point of view and have made the best offer we can make.
"I'm sure he can better that offer elsewhere, I'm positive about that - there are plenty of people out there who would like to grab Morten on the basis of his experience and his capability of playing.
"Being on a free transfer could bring far greater financial advantage than probably we have offered.
"But hopefully he will balance that against the fact that he's had a great career here and that he's a regular.
"It's ever more difficult to find a footballer capable of playing in the Premier League so when you already have one you do your very best to keep him.
"It is in his hands now, our offer has been made - the ball is in Morten's court."
Now Wolves are just about safe, there will be little at stake in tomorrow's match at Molineux apart from league places, and Rovers can still finish in the top half of the Premier League.
Allardyce has his eye on 10th spot but is also likely to use the match to freshen up his starting line-up - it may, for example, be an opportunity for Turkish midfielder Yildiray Basturk to stake his claim for a contract for next season.
"Finishing in the top half of the table is a priority but it's also a chance to use some of the other players," said Allardyce.
"For example Phil Jones has burst on to the scene and that experience will be invaluable to us next season.
"We are not wanting to weaken side but hopefully some other players can show what they can do and we could try a slightly different system."
Blackburn will be without Chris Samba (groin) and Brett Emerton (hamstring) while El Hadji Diouf is doubtful after suffering from tonsilitis.
Allardyce had some words of praise for his opposite number at Wolves, Mick McCarthy, for managing to keep the west midlands side in the top flight.
He added: "Mick has had a varying career in management and all his experience is one of the reasons why they are going to survive in the Premier League.
"He has stuck by his ideas, pushed the side forward and has done the right thing for Wolves despite some criticism."
Source: Team Talk
Source: Team Talk