The England international has been told he can leave The Emirates this month, and Everton have always been favourites to land him.
But Allardyce says he won’t get too excited until the player signs on the dotted line.
He said, “If that is possible to get over the line I would be delighted but obviously there is negotiations that are happening at the moment.
“If that can all be sorted out, which is one of the most difficult things to do then that would be a great addition in my opinion to come and join us from an attacking point of view.
“If that is at all possible it would be very nice, but it is not imminent at the moment but some negotiations are going on.
“It is permanent we are hoping to negotiate. I don’t think there is any chance of a loan.
“I will be very excited and enthused once somebody, if it is not Theo then somebody else, has signed on the dotted line.
“In this window you don’t get too optimistic because so many things can happen in a short space of time.
“You will never think a player is coming until somebody tells you he has actually signed on the dotted line.”