Stelios Giannakopoulos has warned Bolton they risk losing him unless they speed up new contract talks.
Stelios says he knows Liverpool want him and he could be tempted, if Wanderers don't get a move on.
"It is not speculation," he said of the Liverpool link. "It is a true situation. Liverpool wanted me and, maybe, they still want me. I don't know.
"So I have to know, the earlier the better, so that I can be settled in my mind.
"I am not saying I am not settled in my mind with Bolton now, but the earlier you finish these situations, the better it is for the player and for the fans, because the fans keep coming and asking 'Is Stelios staying or going?' and I don't know the answer.
"While the situation is not finished and the transfer keeps going, you never know what's going to happen.
"That is why I am saying it has to be finished so that we know what is going on."
Stelios says he would be only too pleased to stay at the Reebok, if his contract situation can be resolved quickly.
"Of course I am very happy here," he said after making his first pre-season appearance with a 56-minute runout in the 1-0 defeat at Hull on Saturday.
"You can see on the pitch that I am happy, from the football that I play.
"I enjoy it here. Everybody loves me and I love everybody, so it is a good relationship."
Allardyce, meanwhile, has denied any interest in Valencia's Uruguayan international, Gonzalo De Los Santos. "I don't know who he is," he said of the experienced midfielder.