Allardyce blasted Hull City owner Assem Allam for trying to change the club's name, claiming West Ham's owners would never mess with tradition like that.
He said: "There's absolutely no chance of that happening whatsoever with David Gold and David Sullivan.
"Owners are entitled to do what they want but when it comes to messing with the history and tradition of the club I think they have to be mindful of how much it means to people.
"I think it shouldn't be messed with. It should be left well alone. Why cause unrest with your fans when they should be enjoying their season?"