Speaking at the 75th United Nations General Assembly on Friday (local time), Morrison asked the worldwide community to seek an answer as to how the virus was transmitted to humans.
"This virus has inflicted a calamity on our world and its peoples. We must do all we can to understand what happened for no other goal than to prevent it from happening again.This is a global responsibility and it is a moral responsibility for a vaccine to be shared far and wide", he said.
US biotech firm Inovio Pharmaceuticals also said it was not involved while Johnson & Johnson said it was evaluating the potential benefit of a human challenge trial but would not comment on the British plans.
Australia's call for an investigation has contributed to a sharp deterioration in relations with China, whose ties have also soured dramatically with the United States.
The FT report said that the volunteers for the project, which will be announce next week, will be first inoculated with a vaccine and later receive a challenge dose of the Covid-19 causing SARS-CoV-2 coronavirus, under controlled conditions.
Upset by Australia's support of the independent coronavirus investigation, Beijing imposed retaliatory trade restrictions on Australian products, such as barley and wine, starting in May.
One of three Chinese companies with vaccines in the last stages of testing, Beijing-based Sinovac will prioritize nations conducting its Phase III trials, and then offer doses to regions hard hit by the coronavirus, cief executive officer Yin Weidong said during a government-organised media tour of the company's facilities.
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'As an outward-looking, sovereign, trading nation, Australia also values the rules and institutions that enable worldwide trade, ' Mr Morrison said. "This is a global responsibility, and it's a moral responsibility, for a vaccine to be shared far and wide", he said.
US President Donald Trump's administration has given notice that the United States will pull out of the World Health Organisation, calling it biased towards China, and has refused to promise to share Covid research, fearing theft of intellectual property from US pharmaceutical companies.
President Xi Jinping in May promised that China-developed vaccines will be a global "public good" that can be shared by all.
Beyond Blue's Coronavirus Mental Wellbeing Support Service is a 24/7 service free of charge to all Australians.
The Prime Minister also said there is a "clear mandate" for Australian-led efforts to push for an global investigation into the origins of the coronavirus.
The researchers said more details on safety and effectiveness will follow when the study is completed.
Mr Morrison said the World Health Organisation must assist in helping distribute the vaccine.