The veteran goalkeeper is entering the final year of his Reebok Stadium contract and is keen to extend the deal.
However, Jaaskelainen appears frustrated at the inactivity from Bolton with a source telling The People: "Jussi is unhappy. He's in the last year of his contract and nothing is happening about a new deal."
Manchester City are said to be looking for an experienced back-up goalkeeper to support Joe Hart, and could be keen on 36-year-old Jaaskelainen. City are also said to be eyeing Stoke's Thomas Sorensen.
Bolton have already sold Ali Al-Habsi to Wigan this summer, leaving 23-year-old Adam Bogdan as their only other goalkeeper.