Crossbench senators David Leyonhjelm and Bob Day will formally approach the Palmer United Party's Jacqui Lambie on Monday to propose forming a new voting bloc in the Senate.

In an interview with Fairfax Media, Senator Leyonhjelm spelled out how the proposed new voting bloc would work, saying he would be happy for his staff to assist Ms Lambie with bills and senate procedure.

"It would be, 'Let's put our heads together on individual bills'," the Liberal Democrat senator said.

The meeting has been spurred by Senator Lambie's public and heated clashes with PUP leader Clive Palmer.

Senator Leyonhjelm said: "We would brief her staff [on] how we were going to vote, but on the big issues when we wanted to [put the government under pressure] we would get together and agree on a position. But it would be issue by issue.