Liverpool mayor Joe Anderson has informed British sports minister Tracey Crocuh that the city would have "no problem" being ready four years earlier than intended.
Smith said there would not be a bidding process for 2022, rather the federation would approach cities it knew were ready-made for the job.
The host city would need a range of facilities that were ready, and could put together a significant amount of money in short order.
"We wouldn't want to be starting from scratch," she said.
Gold Coast will host in 2018 but she said it was unlikely the same city would go back-to-back. Smith said it was a "fundamental part of the movement" that the Games were held every four years, and the federation would not want that continuity to be broken.
Mayor Phil Goff has already ruled out the Auckland taking on the 2022 assignment, saying the city was already under enough financial and infrastructure pressure.