Twitter has another potential suitor as it mulls whether to accept Elon Musk's offer to buy the company.

The Wall Street Journal, citing people familiar with the matter, said that buyout firm Apollo Global Management is thinking about participating in a bid for Twitter. It could support Musk or another firm such as private equity firm Thoma Bravo, which is reportedly interested in acquiring Twitter as well.

Musk, who is one of Twitter's largest shareholders, offered to buy the company for $54.20 per share. The offer would value Twitter at $43 billion. Some analysts, though, think that it's unlikely Twitter will accept Musk's deal. Last week, Twitter adopted what's known as the "poison pill" defense, making it more expensive for a potential buyer like Musk to acquire the company. Still, the company said that this tactic doesn't prevent the board from accepting an acquisition proposal or engaging with other parties if the board thinks it's in the best interest of the shareholders.

Apollo Global Management, which owns Yahoo, didn't immediately respond to a request for comment.

Musk, who is an avid user of the service, has expressed interest in buying Twitter because he thinks the company isn't adhering to the principles of free speech. Twitter has been criticized for how it moderates content, but the First Amendment applies to government censoring speech, not companies.