Baron told the Telegraph: "The key will be winning the support of the southern hemisphere unions but with everyone facing horrendous financial challenges, this is a bold and ambitious plan to raise large amounts of new cash from which they will be major beneficiaries."
Baron helped England win hosting rights for the 2015 World Cup and said that tournament generated profits around $800m.
All profits from the proposed 2021 tournament would be spread around the participating unions, and a support fund started for rugby families who had lost members to COVID-19.
"The RFU (England) should take a leadership position and propose to other major unions and World Rugby that a special one-off tournament be held," Baron said.
"Its key selling point is that all the money raised would be for keeping the game of rugby alive around the world.
"I have talked to one or two senior colleagues and they all think the country would get right behind it."
England predicts it will lose more than $200m in revenue if this year's autumn internationals are cancelled. World Rugby has already created a $160m rescue package.
The British and Irish Lions' eight-match tour of South Africa starting in early July would need to be postponed, to protect the professional club competitions around the world.