The social media company had been expected to shoot down the offer and had adopted a so-called poison pill to fend off a potential hostile takeover.
But executives are now re-examining the bid and are more likely than before to try and negotiate, the paper said, citing people familiar with the matter. The situation is fast-moving, but the two sides are meeting on Sunday to discuss Musk’s $43 billion proposal, the Journal reported.
Twitter did not immediately respond to CNBC’s request for comment on the report.
The social media giant is reportedly still working on estimating its own value. Executives could also insist on guarantees, such as Musk covering breakup protections if the deal fell through, the paper said.
Twitter is set to report its latest financial results on Thursday and had been widely expected to weigh in on the bid then. Executives could also discuss the deal earlier in the week, the sources said.
Twitter could indicate it is open to other bidders or negotiating with Musk on certain terms, according to the report. Musk has reportedly said he will not sway from his initial offer.