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.
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.
He is likely to stick with Harper for the trip to Manchester City tomorrow but said: "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.
But he is refusing to look beyond the end of the season and a cash offer in January would leave Wanderers in a dilemma.