Paramount on Wednesday decided to extend its deadline to evaluate a takeover bid from the media executive Edgar Bronfman Jr., the company said, a sign that the company is taking the offer seriously.

The bid, submitted at the 11th hour, could shake up the company’s existing deal to be acquired by Skydance, an up-and-coming Hollywood studio. The $8 billion deal with Skydance was reached after months of negotiations. That deal is backed by Larry Ellison, the Oracle founder, whose son, David, runs Skydance.

“There can be no assurance this process will result in a superior proposal,” the company said, adding that it “does not intend to disclose further developments unless and until it determines such disclosure is appropriate.”

Mr. Bronfman and Skydance declined to comment.

Mr. Bronfman and his backers will now have until early September to convince a special committee of Paramount’s board of directors that their offer is superior. Skydance also has the right to improve its bid to beat other suitors, which could further prolong the process.

Mr. Bronfman has assembled a group of investors that includes deep-pocketed private equity firms like Fortress Investment Group and a crypto kingpin who starred in a film from the “Mighty Ducks” franchise. Collectively, they have proposed to pay $6 billion for a controlling stake in National Amusements, Paramount’s parent company, along with a minority stake in the media conglomerate.

The Wall Street Journal earlier on Wednesday reported updated details of Mr. Bronfman’s offer.

The bidding group also has ties to people associated with Shari Redstone, Paramount’s crucial controlling shareholder. Jonathan Miller, who partnered with Ms. Redstone at an investment firm, is an adviser to the bid, according to people familiar with the arrangement, who would speak only anonymously because the discussions are private. Mr. Bronfman is also friendly with Ms. Redstone and met with her in recent weeks to discuss his bid, the people said.