London, Liverpool and Birmingham have expressed interest in staging the event after host city Durban pulled out.
Manchester City Council said it was ready "to ensure the delivery of a successful games" if asked.
Liverpool Mayor Joe Anderson said he would be "happy to work with" Manchester.
However, in a tweet he said Liverpool would "challenge" any attempt to "gift the games to London or anyone else without a proper bidding and procurement process".
It is understood Manchester would be willing to act as a host city, or in collaboration with other locations.
The city hosted the games in 2002.
In a statement, the council said: "If we were invited to help, we would be pleased to work with the Commonwealth Games Federation and the government to ensure the delivery of a successful 2022 Games in England."
A spokesman for the Mayor of London said the games are "a wonderful sporting event" and London "would listen to any proposal to host in 2022".
"However there would be a number of practical issues to consider with the government and other stakeholders, including the substantial amount of funding it would require."
Senior officials from Manchester have been in talks on the city helping to host the 2022 Commonwealth Games, the BBC understands.