Jaaskelainen, 30, was linked with a move last summer but appeared to have settled his future when he agreed a three-year contract extension.
But the stopper never put pen to paper - and with 18 months left on his current contract, Allardyce accepts the club may have to cash in or risk seeing a key player go for free.
"It is true we have not resolved our contract negotiations with Jussi," Allardyce told the club's official website.
"The situation is one that looks like it might not be resolved from a legal point of view.
"There is a stand-off in terms of a legality of a contract that other players have signed here.
"At the moment, he doesn't want to sign, and we don't believe that we should give him something different to what other players have signed here.
"Jussi is a valuable asset and if he isn't going to sign his contract, then the club may wish to cash in at some stage.
"That could be in January or at the end of the season if we have not resolved the situation."
"Jussi's agent tells me he has a club for him but that club haven't made an offer. So can we say that there has been an illegal approach for him?
"Is that why he hasn't signed?"