Adam Aron, the AMC chief executive, said in a statement, “Talks are underway with Netflix about our showing ‘The Irishman’ and other Netflix films, but the outcome of those conversations is not yet clear.”

AMC and Cineplex are negotiating with Netflix separately, the people familiar with the talks said. A crucial sticking point has been the major chains’ insistence that the films they book must play in their theaters for close to three months while not being made available for streaming at the same time, which does not sit well with Netflix. Talks broke down in July, only to pick up again two weeks ago, the people said.

Netflix, Mr. Scorsese and Cineplex declined to comment for this article.

Because of the impasse over the three-month theatrical window, Netflix has yet to give any of its films the kind of blockbuster theatrical releases that companies like AMC can provide. The streaming giant’s reluctance to concern itself with weekend box-office numbers reflects its laser focus on its main mission: delivering streaming video on demand to its 151 million subscribers worldwide.

Having built itself into an entertainment powerhouse by keeping its subscribers interested and coming back for more, the company does not want to be distracted by the demands of the old-style movie business, even as it makes deals with legendary filmmakers like Mr. Scorsese.

“Netflix is in the subscriber happiness business,” said Richard Greenfield, a tech and media analyst. “They need to attract more members and make current members happier. ‘The Irishman’ is really important.”

Many Netflix movies, like the Adam Sandler vehicle “Murder Mystery,” which Netflix said had 78 million household views in its first four weeks, seem made for living-room viewing. But Netflix has also come out with more ambitious offerings, like “Roma,” the meditative black-and-white film from the director Alfonso Cuarón. “Roma” won praise from critics on its way to three Oscars this year, for best director, best cinematography and best foreign language film.