Richard Plepler was an Emmy magnet when he was in charge of HBO, with a knack for betting on shows that pleased critics and added subscribers. Now he is in the final stages of talks to produce television shows and documentaries for the new Apple TV Plus streaming service, according to two people with knowledge of the talks .

Mr. Plepler left HBO in February, chafing under his new bosses eight months after AT&T became the cable network’s parent company. Over the last few months, he has been preparing to open a production company, working out of an office in a townhouse on the Upper East Side of Manhattan.

Mr. Plepler and a representative for Apple declined to comment.

If the deal comes to fruition, according to the people, Mr. Plepler will make projects exclusively for Apple TV Plus, which had its debut on Nov. 1. Some critics have noted the similarity between Apple’s approach to programming and the strategy followed by HBO on Mr. Plepler’s watch. The new service offers a mix of dramas led by name actors and award-winning producers, grand spectacles and edgy comedies.

The Wall Street Journal reported the news of the negotiations first.

Mr. Plepler, who had worked at HBO since 1992, was a co-president of the premium cable channel before becoming chief executive in 2013. While he was in charge, HBO won more than 160 Emmys. The biggest hit of the Plepler years was “Game of Thrones,” a big-budget fantasy that won 59 Emmys during its eight seasons.