The Reds had been rumoured to have put in an offer of up to £400,000 for the young stopper after a Lyn director described the Wanderers initial transfer offer as "derisory".
Oman international Al-Habsi has been tracked by both clubs for a number of months and underwent a trial period at the Reebok Stadium earlier on in the season.
Agent Peter Harrison who is representing the player said: "Bolton have withdrawn their offer to Lyn for Ali and he is now going to stay at Lyn, he will see out his contract at Lyn and he will be able to talk to interested clubs in July and sign a pre-contract with whoever offers the best deal.
"There are a number of clubs who are keeping tabs on him as he is best goalkeeper in Norway."