Birmingham, Liverpool, London and Manchester have expressed interest in staging the Games in place of Durban.
Durban was due to be the first African city to host the games but was stripped of the right on Monday.
Commonwealth Games Federation chief David Grevemberg said officials were looking to make a decision quickly and would consider a joint bid.
"We are interested in looking at different delivery models and part of our strategic plan is to look at more affordable and appealing structures for hosting major events," said Grevemberg.
"There is a possibility in the future that we could look at combined events but at this point in time we are trying to ensure we deliver the best possible Games in the best possible city.
"Right now we are not speculating on any specific candidates over another.
"We really need to look over the context, time available, infrastructure, what is the resourcing base and ensure that we are able to have a good fit and a good partner." - BBC -