South Korea's biggest cinema chain is reportedly lining up a £2bn bid for Vue Cinemas - which has screens in Lancaster and Barrow.
CJ-CGV has appointed investment bankers to look into a deal.
Vue's owners have also been considering floating the company, and will be hoping news of the interest will begin a bidding war among competitors.
At the start of this year, the ticket prices at Lancaster were cut by 50% for any film at any time, following fears for the chain's future.
A Vue spokesman at that time said: “Vue has selected a cross section of sites across the UK for this promotion.
“The idea is to give those areas a big screen experience for just £4.99.”
CJ-CGV bought Turkey's Mars Cinema for $800m two years ago, expanding its cross-border reach beyond China, Hong, Kong, Indonesia, the US and Vietnam.
It was unclear on Monday whether the Korean operator would be prepared to meet the asking price of Vue's current owners, which could be £2bn or more.
Vue recently appointed the former ITV chief executive Adam Crozier as its chairman, augmenting its credibility as a potential publicly listed company.
Tim Richards, Vue's founder and chief executive, has grown the business from a UK-only operator established in 1999.
He said in a recent newspaper interview: "We are truly the last port of call if an international operator wants to come into Europe.
"There are international distributors in North America, Korea, Japan, Mexico and Australia: these are groups that we know and we would want to work with."