“You would think 2027 would need to go somewhere southern hemisphere,” Sweeney told BBC Sport.
“Australia is a really important rugby nation, who have had some financial challenges.
“Anything that World Rugby can do to support the game in Australia would be supported by all of us, I think.”
The RFU’s backing would be significant for Australia, with strong European nations traditionally voting as a bloc.
France will stage the 2023 edition, making it the third straight northern hemisphere host after England (2015) and Japan (2019).
World Rugby plans to name the two subsequent hosts simultaneously, probably in late 2021.
Rugby Australia announced a government-backed bid last December, hoping to add to its only sole staging of the tournament, in 2003. It co-hosted the inaugural event with New Zealand in 1987.
Argentina and Russia are also formally in the race for 2027 while it is expected South Africa will bid and become a front-runner, having narrowly missed out to France to stage the next tournament.
The United States was originally considered a strong contender but being the main host of the 2026 FIFA World Cup and staging the 2028 Los Angeles Summer Olympics may count against a bid.
A commercially-strong, US-hosted Rugby World Cup in 2031 was endorsed by Sweeney.