Diouf has been at the centre of controversy ever since his arrival in England back in the summer of 2002 and Allardyce believes that Bolton are the only club who will want to take a gamble on him.
"Any time he spits on a football pitch now, someone is going to complain, Somewhere down the line we're going to have to decide whether we want to put up with that on a permanent basis.
Allardyce confirmed that he had recieved no indication from Liverpool as to whether a permanent deal could be struck, but he is hoping that the Merseysiders cut their losses on a man who cost them £10 million from French club Lens.
"Liverpool have not given any indication as to what he would cost, but I would have to think they will have to let him go for nothing. After all that has gone on with him, I think we're the only club that would consider taking him.
The Wanderers chief has also called for more consistency from the two times African Player Of The Year and says that there is still room for improvement in building on recent performances.
"He has scored twice in two games now, but I wouldn't say he is boosting his value. I don't think he has played that well and another issue is whether he can become more consistent."