Odeon owner AMC is in "urgent talks" with Warner Bros after the film maker said all releases would be available to stream instantly in the US.
The move will enable film fans to watch the forthcoming sci-fi epic Dune and the Matrix sequel on HBO Max at the same time as their cinema release.
It has escalated tensions between Hollywood and US movie theatres.
Both studios and chains are desperate to rebuild revenues after virus control measures closed cinemas.
The new releases will be available on the service, which is not yet available in the UK, for one month after release. HBO Max is set to launch in Europe in the second half of next year, according to its global boss Andy Forssell.
The releases are also expected to include Godzilla vs Kong, Mortal Kombat and The Suicide Squad.
Earlier this year, assertive action by AMC successfully curbed a similar screening plan by rival Hollywood studio, Universal.
Cinemas are desperate for content to lure viewers back with new entertainment that can initially only be seen on their screens.
Typically, new releases are shown exclusively at cinemas for months.
AMC had agreed to allow one film, Wonder Woman 1984, to be shown simultaneously on HBO Max, the streaming service owned by its ultimate parent company AT&T.
AMC boss Adam Aron, said: "These coronavirus-impacted times are uncharted waters for all of us, which is why AMC signed on to an HBO Max exception to customary practices for one film only, Wonder Woman 1984, being released by Warner Brothers at Christmas when the pandemic appears that it will be at its height."
It accused Warner Bros of subsidising its HBO Max by its move: "We will do all in our power to ensure that Warner does not do so at our expense. We will aggressively pursue economic terms that preserve our business.
"We have already commenced an immediate and urgent dialogue with the leadership of Warner on this subject."
Ann Sarnoff, chair and chief executive of WarnerMedia Studios, said the pandemic called for "creative solutions".
"No one wants films back on the big screen more than we do," she said.
"We know new content is the lifeblood of theatrical exhibition, but we have to balance this with the reality that most theatres in the US will likely operate at reduced capacity throughout 2021."
AMC banned all Universal films after the studio said it would release new movies at home and on the big screen on the same day.
The two firms eventually agreed that Universal films can go to digital services after just 17 days of viewing in cinemas.
Explaining Warner Bros' decision, Ms Sarnoff said the "unique one-year plan" would give "moviegoers who may not have access to theatres, or aren't quite ready to go back to the movies, the chance to see our amazing 2021 films".
"We see it as a win-win for film lovers and exhibitors, and we're extremely grateful to our filmmaking partners for working with us on this innovative response to these circumstances."