Pedersen is out of contract in the summer and has yet to make a decision on his future.
“We have gone as far as we can from a financial point of view and have made the best offer we can make,” said the Rovers boss.
“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.”
He added: “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.”
