Maybe they know your previous salary, but they don't know how many offers you have. You just have to put your foot down and say you won't move if they offer les

Maybe they know your previous salary, but they don't know how many offers you have. You just have to put your foot down and say you won't move if they offer less than X and state that you current salary is irrelevant as they up against other companies not your current one. I managed to get a significant salary bump even without having a job, because I made sure they understand from the beginning I'm happy to walk away.