There is a "very high chance" former Labor leader Mark Latham will run under a Liberal Democrats banner at the next state or federal election.

Mr Latham had renounced a return to politics after quitting the Labor leadership, but Liberal Democratic senator David Leyonhjelm confirmed discussions with him were ongoing.

"There's a very high chance he'll be running for us somewhere at either a NSW or federal election, or possibly both," Senator Leyonhjelm told AAP on Saturday.

"He's also on a political journey bringing him pretty close to the position and principles of the Liberal Democrats."

Mr Latham joined the Liberal Democrats in 2017, saying at the time that he supported "80-90 per cent" of the party's platform.

He has been helping the party establish new branches, while discussing the possibility of running as a candidate with its national executive.

Senator Leyonhjelm confirmed discussions had canvassed state and federal, upper and lower house options.

Mark Latham. (AAP) (AAP)

"It does appear as if he is interested in returning to politics," he said.

"We've had discussions with him about where and how."

But nothing was locked in, he said, adding his party was waiting on Mr Latham to come to a decision.

On Friday, Mr Latham declined to confirm if One Nation has also asked him to replace ousted Senator Brian Burston.

"I've been approached by representatives of four different parties wanting me to run in the senate," Mr Latham told the Nine Network.

"I'm not going to be talking about private conversations."

According to Senator Leyonhjelm, Mr Latham occasionally enjoys leading on the media as "good sport".

"Mark enjoys winding up the media," Senator Leyonhjelm said.