Mr. McMahon, whose abrupt departure in July 2022 followed disclosures by The Wall Street Journal of multiple payouts to women who had alleged sexual misconduct and infidelity, expects he will be able to assume the role of executive chairman, though he would need board approval for that, the people said.

It isn’t clear where that would leave his daughter, Stephanie McMahon. After his departure, she took over as chairwoman and co-CEO alongside

Nick Khan,

the company’s former president.

The 77-year-old sent a letter to WWE’s board in late December detailing his desire to return to the company he ran for four decades, to help spearhead a strategic-review process, the people said. Mr. McMahon believes there is a narrow window to kick off a sales process because WWE’s media rights—including for its flagship programs “Raw” and “SmackDown”—are about to be renegotiated, according to the people.

Mr. McMahon believes the media landscape is evolving quickly and more companies are looking to own the intellectual property they use on their streaming platforms, making WWE an attractive takeover target, the people said. WWE, which generates most of its revenue from selling content rights, posted its first year of over $1 billion in revenue in 2021. The company currently has a market value of just over $5 billion.

The board responded last month in a letter to Mr. McMahon that it was prepared to initiate a review process and would welcome working with him on it. However, it said it unanimously agreed that Mr. McMahon’s return to the business wouldn’t be in shareholders’ best interest, according to people familiar with the letters.

The board also asked Mr. McMahon to confirm his commitment to repay expenses incurred by WWE related to an investigation of the allegations and requested that he agree not to return to the company during government probes of the matter, the people said. Mr. McMahon said in response that he remains willing to continue working to complete any reimbursement for reasonable expenses related to the investigation, to the extent they aren’t covered by insurance, but he declined to agree to not return to the company.

He has communicated to the board that unless he has direct involvement as executive chairman from the outset of a strategic review, he won’t support or approve any media-rights deal or sale, the people said.

Mr. McMahon retired as WWE chief executive and chairman in July amid a board investigation of sexual-misconduct claims against him. The Journal reported that he had agreed to pay more than $12 million in secret settlements since 2006 to his accusers.

The Securities and Exchange Commission and federal prosecutors launched inquiries into the payments. WWE later disclosed additional payments in 2007 and 2009 totaling $5 million that it said were unrelated to the allegations of misconduct that led to its internal investigation.

WWE’s board ultimately found that the payments, though made by Mr. McMahon personally, should have been booked as WWE expenses because they benefited the company.

Mr. McMahon had told people that he intended to make a comeback at WWE, the Journal reported last month. He said that he received bad advice from people close to him last year to step down, according to the people familiar with his comments.

—Joe Palazzolo and Ted Mann contributed to this article.

Write to Lauren Thomas at lauren.thomas@wsj.com