Thoma Bravo, a private equity firm that had more than $103bn in assets under management as of the end of December, informed Twitter that it is exploring the possibility of putting together a bid, the sources said.
It is not clear how much Thoma Bravo would be prepared to offer and there is no certainty that such a rival bid will materialise, the sources cautioned, asking not to be identified because the matter is confidential.
The New York Post reported on Thursday that Thoma Bravo was considering a bid for Twitter.
In an opinion poll floated on Twitter by billionaire Elon Musk, 83.5 per cent of those who voted said the decision to take the microblogging platform private should rest with the shareholders of the company and not the board. The other 16.5 per cent were in favour of the board making the final call.
Mr Musk, founder and chief executive of electric vehicle maker Tesla and rocket company SpaceX, took to Twitter early on Friday and posted a poll: “Taking Twitter private at $54.20 should be up to shareholders, not the board,” with two options, ‘Yes’ or ‘No’.
Later on Friday, Twitter made a move to shield itself from a takeover bid by Mr Musk. The company's board adopted a limited-duration shareholder rights plan, which would enable its shareholders to buy additional stock.
Under the plan, also known as a 'poison pill' strategy to resist a bid from a potential acquirer, "the rights will become exercisable if an entity, person or group acquires beneficial ownership of 15 per cent or more of Twitter's outstanding common stock in a transaction not approved by the board", Twitter said in a statement.
The plan, which will expire in a year, "does not prevent the board from engaging with parties or accepting an acquisition proposal if the board believes that it is in the best interests of Twitter and its shareholders".
Saudi Arabian billionaire Prince Alwaleed bin Talal, who owns a stake in Twitter through his Kingdom Holding Company, rejected Mr Musk’s Thursday offer, saying the proposed offer did not “come close to the intrinsic value of Twitter given its growth prospects”.
“Being one of the largest and long-term shareholders of Twitter, Kingdom Holding Company and I reject this offer,” Prince Alwaleed said on Twitter.