Mr Morrison will put the plan to premiers and chief ministers in the hope of creating a unified approach to removing the barriers as coronavirus case numbers fall below agreed benchmarks.
Unable to force the states and territories to scrap their border checks,the Prime Minister will instead argue for an"exit plan"so Australians know there is a plan to relax the measures that have stopped tourism and trade.
The national cabinet has fractured over the controls,with premiers making unilateral decisions to close borders and offering no consensus or agreement on how or when to unwind the measures.
Mr Morrison is seeking to avoid a fight over the plan but is seeking a deal at a time of heightened tension with Victorian premier Daniel Andrews over the blame for infections in hotel quarantine,aged care and the wider community.
"What is really important now as we go forward is there is no dispute from the Commonwealth about the powers that the states and territories have,"he told Parliament on Monday.
"When it comes in relation to borders,there is no dispute about those powers.