The deal is yet to be confirmed and Allardyce is still optimistic he can persuade the 34-year-old midfielder to stay in North West England.
He told the club's official website: "You can't rule us out. We are very interested in signing Roy.
"The chairman [Phil Gartside] will contact Keane's representatives in the next couple of days with our offer.
"He would be a tremendous signing for Bolton and I'm very excited about the prospect."