Apollo Global considers participating in a bid for Twitter

Apollo, one of the world’s largest buyout firms, has held discussions about backing a possible deal for Twitter and could provide Mr. Musk or another bidder like private-equity firm Thoma Bravo LP with equity or debt to support an offer, the people said.

Apollo, which owns Yahoo, has also been evaluating potential cooperation between the online-media company and Twitter, the people said. There is no guarantee Twitter would be receptive to that, or any other deal.

Twitter is expected to rebuff Mr. Musk’s offer in the coming days, some of the people said. The company is set to report earnings April 28 and may detail its stance then.

Either way, Apollo’s interest adds to a list of Wall Street heavyweights, including Morgan Stanley, lined up to support a deal for Twitter, which despite the popularity of its platform has struggled to grow.

Private-equity firms including Thoma Bravo are circling Twitter, people familiar with the matter said last week after Mr. Musk launched his surprise bid.

There is no guarantee any private-equity firm will end up making a firm bid, whether for the entire company or just a portion, and there may well be no deal in the end—with Mr. Musk or anyone else.

Taking Twitter private would rank as one of the largest leveraged buyouts of all time, and the company doesn’t have the attributes of a typical LBO target like strong, stable cash flow.

New York-based Apollo is a private-equity and lending behemoth with roughly $500 billion under management, known for buying companies in a range of sectors including media and for its big insurance arm. The firm often invests across a company’s capital structure, providing preferred equity or debt, in addition to doing straightforward buyouts.

Thoma Bravo, a technology-focused investor that manages about $100 billion, has historically relied almost exclusively on private-credit financing for its deals, including its recent $10.7 billion deal for software-maker Anaplan Inc.

Mr. Musk, the billionaire Tesla Inc. chief executive, owns a more than 9% stake in Twitter. In recent weeks he has been criticizing how it is run, including its approach to content moderation, which he has argued impedes free speech.

Mr. Musk’s $54.20-a-share bid lacked details on how he would pay for the deal, though The Wall Street Journal reported that Morgan Stanley would provide at least some debt financing, and the billionaire entrepreneur has been approached by unnamed investors interested in participating. Existing Twitter shareholders supportive of Mr. Musk could also roll over their holdings into any deal.

Although he is the richest person in the world with an estimated fortune of $250 billion or more, Mr. Musk is cash poor, with nearly all his wealth tied up in shares of Tesla and SpaceX, his privately held rocket company.

Twitter has said it is reviewing Mr. Musk’s bid, which he called his “best and final” offer. On Friday, Twitter installed a poison pill, a legal maneuver meant to dissuade Mr. Musk from substantially increasing his stake while the company reviews his bid.

Should Mr. Musk build a stake of 15% or more in Twitter, the pill would give all other shareholders the right to buy deeply discounted stock, diluting his stake and making building it more expensive. The company detailed the mechanics of the pill in a filing Monday.

Meanwhile, Mr. Musk has continued trolling Twitter on its own platform. On Saturday, he tweeted, “Love Me Tender” with music note emojis, in an apparent reference to Elvis Presley’s hit song. Many viewed it as Mr. Musk signaling his intent to launch a direct appeal to Twitter’s shareholders in the form of a tender offer. If he goes that route, shareholders would have the option to tender their shares at his offer price.

Twitter shares were little changed last week following Mr. Musk’s bid, typically a sign that a proposed deal isn’t garnering investor enthusiasm. They rose 7.5% Monday, closing at $48.45, and over 1% in after-hours trading following the Journal’s report on Apollo’s interest.