PUP could take Lazarus to High Court

The Palmer United Party is considering taking High Court action against Glenn Lazarus after the senator quit its ranks.

The party's national director Peter Burke says discussions are underway with the Democratic Labour Party, which is pursuing Senator John Madigan following his resignation last year.

"Clearly voters put the Palmer United Party before Mr Lazarus and we do not believe he holds the seat on his own merits," Mr Burke said in a statement on Monday.

Mr Burke said PUP received more than 250,000 votes "above the line" in the Senate election and only 6770 votes went "below the line" to Senator Lazarus.

However, constitutional law expert George Williams told AAP the argument had little or no prospect of success.

The argument relies on section 15 of the constitution, which says that when a senator vacates their seat, the state parliament must appoint a replacement from the party that had endorsed the senator at the time of his or her election.

Prof Williams said the section only applied if the place of a senator becomes vacant before the expiration of his or her term of service.

"This occurs if a senator dies or resigns their place in the Senate," he said.

"It stretches the bounds of plausibility to suggest that their seat becomes `vacant' if they merely resign their party membership."

He said the law provided no remedy to a political party when one of its senators leaves the party.