The Sun says Finland international Jaaskelainen, 32, is refusing to sign a new deal at Bolton and will be a free agent at the end of the season. And Allardyce will coax him to St James' Park.
Given Out - Jaaskelainen In? RUBBISH!
He has spent the last 10 years with Wanderers, most of it under the current Newcastle boss.
Ex-Bolton boss Allardyce admitted this week he will struggle to keep Shay Given happy with life on the bench as he is not currently first choice.
Allardyce: "Will Shay be happy on the bench? He cannot be. Impossible."
Bolton are still hoping to persuade Jaaskelainen to commit his long-term future to the Reebok and he is due to be handed a testimonial.
A cash offer in January would leave Wanderers in a dilemma, because obviously they wouldn't get a penny for him in the summer.