He is working to establish an international coalition to drive change to ensure lessons are learnt from the coronavirus pandemic.
The ABC reports that the government believes overhauling the WHO is too tricky a task and so establishing a brand new body is a more realistic approach.
Morrison held calls with United States President Donald Trump, French President Emmanuel Macron and German Chancellor Angela Merkel.
According to the ABC, the three leaders are supportive of Morrison's plan.
The PM also spoke to billionaire Microsoft founder turned philanthropist Bill Gates, whose foundation is the largest private financial support of WHO.
The body's conduct in recent months was raised during that conversation, it's understood.
Australia is unhappy with the way WHO has handled the coronavirus outbreak, which has so far infected 2.5 million people globally and caused more than 177,000 deaths.
WHO has been criticised for responding too slowly to the emergency and for accepting without question China's downplaying of the outbreak in Wuhan and the subsequent rapid spread.
China's influence over the organisation has also been criticised.
Foreign Minister Marise Payne has separately called for a global inquiry into how the pandemic originated and the handling of the pandemic.
That suggestion has sparked anger from Beijing and it has vowed to fight any effort to investigate its response.
The US pays for about 20 per cent of the WHO operating budget and last week suspended its funding.
