Diouf has recently returned to some form at the Reebok Stadium, and it is thought Rafa Benitez would let the Senegalese player go for the right price.
But with spitting allegations and flare ups a regular occurence, the Bolton boss has said he isn't sure when the next problem is going to happen.
Allardyce said: "With him we don't quite know when the fuse is going to blow and that's a concern, not just for me but for the owners of this football club."
He added: "To splash out on a big contract for a player of his calibre is a big decision and we will make it at the end of the season. If you took him on it would be a gamble because he could flare up again."