As first reported in the Sunday Times, the firm is writing to Prime Minister Boris Johnson and Culture Secretary Oliver Dowden to say the industry is now "unviable".
The firm says it has been hit by delays in the release of big-budget films, putting 5,500 jobs at risk.
The premiere of James Bond film No Time To Die has been postponed twice and is now due for release in April 2021.
It is hoped that the Cineworld cinemas will be able to reopen next year, with staff being asked to accept redundancy in the hope of rejoining the company when theatres open again.
The head of the UK Cinema Association said he feared the Cineworld closure was "indicative of challenges faced by the entire UK cinema industry at the moment".
Phil Clapp said: "Although cinemas opened in July and have been able to deliver a safe and enjoyable experience, without major new titles then we understand we aren't able to get as many people out of the home as we'd like."
He said no-one would be "untouched by the current challenges".
Philippa Childs of entertainment and broadcasting union Bectu said: "The delay in the release of the Bond film along with the other delayed releases has plunged cinema into crisis.
"Studios will have to think carefully when considering release dates about the impact that will have for the long-term future of the big screen."
When approached by the BBC, major UK chains Vue and Odeon refused to comment on how many cinemas they might be keeping open.
The Department for Digital, Culture, Media and Sport said it was supporting cinemas through a VAT cut on tickets and concessions, business rates holiday and bounce-back loans.
"We urge the British public to support their local cinema and save jobs by visiting and enjoying a film in accordance with the [Covid-19] guidance."