Former HBO Chairman and Chief Executive Richard Plepler is in advanced talks to sign an exclusive production deal with Apple Inc . ’s new TV+ streaming service, according to a person familiar with the matter.

Under the terms of the agreement being discussed, Mr. Plepler’s new company, RLP & Co., would create original content for Apple TV+. A deal could be finalized within the next few weeks, the person with knowledge of the talks said. It is still possible a deal may not materialize.

If Apple lands Mr. Plepler, it would be getting one of the most well-regarded entertainment executives of the last decade. Under his watch as chief executive of HBO, the pay channel prospered, developing such hits as “Game of Thrones” and “Veep.”

Apple’s pursuit of Mr. Plepler is indicative of the battle for creative talent among Hollywood giants and the Silicon Valley disrupters such as Netflix Inc . and Amazon.com Inc. All have been spending heavily to woo producers and creators in anticipation of the so-called streaming wars, aimed at wooing viewers when many are tuning out of traditional broadcast and cable television.

Mr. Plepler left HBO last February after new owner AT&T Inc. took control of the company. He had been with HBO for nearly three decades, the last six years as its chief executive. Mr. Plepler left HBO when it was clear that under AT&T he would have less autonomy than he had enjoyed under prior owner Time Warner Inc.