Liverpool and Birmingham have already expressed an interest - as have Sydney and Melbourne in Australia - in replacing Durban, which lost the right to hold the games following a trail of missed deadlines and financial problems.
"Hosting the Commonwealth Games in 2022 could give us an opportunity to step up and show the very best of Global Britain as an outward-looking nation that is confident on the world stage," Culture Secretary Karen Bradley said in a statement.
The government would look at all bids before deciding whether to put in a formal bid later this year, the ministry added.
Durban's problems highlighted the daunting burdens facing host cities for major sporting events.
Africa has never hosted the Games, which take place every four years and bring together athletes from the 52 members of the Commonwealth, most of which were at one time colonies of Britain.
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