Private equity giant Thoma Bravo is working on a possible bid for Twitter, a source close to the situation told The Post — setting up what could be a rival to Elon Musk’s offer for the social giant.

“They are making a push,” the source said of the private-equity firm that already owns tech names including McAfee and Landesk.

It’s not clear what Thoma Bravo might bid or when it would present the Twitter board with its bid. The firm has an internal team working on the potential transaction, the source familiar with the matter told The Post.

“You are not far off,” a second source close to the situation said when asked by The Post if Thoma Bravo was working on a possible bid for Twitter.

Thoma Bravo could be a white knight for the company and CEO Parag Argawal, one of the sources said.

Musk on Thursday made a non-binding offer of $54.20 a share for Twitter, telling the company it was his best and final offer. If the board doesn’t accept his offer, “I would need to reconsider my position as shareholder,” Musk said. Later Thursday he said he wasn’t sure if he’d be able to acquire Twitter.

The Tesla founder and world’s richest man earlier this month revealed he owned 9.2% of the shares of Twitter.

Twitter, if it rejects Musk’s offer, could see its share price collapse unless it had another option to reveal at the time of a possible rejection. That’s where a so-called white knight would come in.

Because of that, Thoma Bravo needs to move quickly — if it elects to move forward — to show the Twitter board it has a potentially friendlier alternative, sources told The Post.

On its website, Thoma Bravo says: “Our private equity investment vehicles employ the same investment philosophy — to partner with and support existing management teams to help deliver solid operating results and drive innovation”.

Musk has in contrast sharply criticized the Twitter management team.

Thoma Bravo invests typically in business-to-business software companies and not companies that cater directly to consumers, like Twitter. In 2020, the San Francisco- and Chicago-based firm announced the closing of a $17.8 billion buyout fund, and through its different vehicles says it has $103 billion in assets under management.

Meanwhile, Twitter generates significant cash flow and is not a bad leveraged buyout candidate, one of the sources said. Thoma Bravo sees potential for the company when it comes to controlling costs and widening profit margins, the source said.

Thoma Bravo last month reportedly reached a $10.7 billion buyout agreement to acquire listed Anaplan, a company that makes software modeling for different business outcomes.

There was a big demand from Thoma Bravo fund investors to co-invest in the deal outside the fund, and many may also co-invest in a much larger Twitter deal, the source said.