Another senator could fall victim to the ongoing citizenship crisis within 24 hours, with Tasmanian independent Jacqui Lambie awaiting urgent advice from British authorities as to whether she is a dual citizen.

Senator Lambie told Fairfax Media she had sought urgent advice last week as to whether she holds dual citizenship, and said she will resign from the Senate immediately if that is confirmed.

"Tasmanians will be the first to know," she said at lunchtime on Monday. She said she hoped to receive the advice within the next 24 hours.

Senator Lambie dismissed the rampant speculation around Parliament House that she was about to resign on Monday afternoon, after Australian Conservatives leader Cory Bernardi told the chamber he knew of another senator under a citizenship cloud.