Paramount CEO David Ellison wants Mark Thompson to continue running CNN after the Warner Bros. Discovery acquisition closes — while Bari Weiss is not expected to have a role at the cable network, according to a report.

The two executives have been negotiating over Thompson’s future in recent weeks, including discussing a new contract, but no agreement has been reached, the Wall Street Journal reported Wednesday.

Thompson’s current deal runs into early next year, according to the Journal.

Thompson wants guarantees that he will remain firmly in control of CNN’s journalism under its new owner, people close to him told the Journal.

Ellison and his team have also been determining how CNN will operate alongside CBS News, which Weiss has led as editor-in-chief through a tumultuous overhaul that included major changes at “60 Minutes.”

Ellison’s current plan does not envision Weiss taking on responsibilities at CNN immediately after the transaction is completed, the Journal reported, citing people familiar with his thinking.

But Weiss is not expected to have a role involving CNN when the deal closes, according to people familiar with Ellison’s thinking cited by the Journal.

The Post has sought comment from CNN, CBS News and Paramount.