Bernardi's plan to stop PM Hunger Games

Fresh from leaving the Liberal Party, Cory Bernardi has a new mission - stop the Hunger Games.

The now crossbench senator has his eyes set on amending legislation to immediately scrap the life gold travel pass for retired parliamentarians.

Under changes announced by Malcolm Turnbull, free travel will be limited to former prime ministers.

But Senator Bernardi wants a tighter requirement placed on the perk - ex-prime ministers who have served four years.

The new crossbencher admits the likes of Tony Abbott, Kevin Rudd and Julia Gillard are his targets.

"Paul Keating I think was the shortest serving prime minister prior to John Howard that would still be eligible for these entitlements of office and I didn't think it was fair to take it away from him, quite frankly," he told ABC TV.

The more recent revolving door of prime ministers had not served the nation well.

"Why would we be rewarding the people who seem to be captaining the ship of state in such a poor manner?"

Senator Bernardi also believes the four-year requirement should apply to another retirement entitlement - staff and offices expenses.

"It will stop the hunger games if you will for people who just want to be able to say 'look at me, I managed to become prime minister whether it be for 12 months, before they're turfed out by their own side," he said.

The gold pass provided former MPs and senators with 10 free return airfares within Australia each year.

Despite being eligible Mr Turnbull has said he won't use the pass once he's out of office.

The Greens agreed to support the entitlements reforms at a partyroom meeting in Canberra on Tuesday.

However, the party will push to amend the bill to ensure former prime ministers are covered by a new independent authority to oversee parliamentary entitlements.

And penalties for erroneous or false claims would be bolstered to what one senior Greens figure said would be "something with bite".

The Labor caucus also on Tuesday agreed to support the reforms.