Twitter had been expected to rebuff the offer, which Mr. Musk made earlier this month without saying how he would pay for it. But after he disclosed last week that he now has $46.5 billion in financing, Twitter is taking a fresh look at the offer and is more likely than before to seek to negotiate, people familiar with the matter said. The situation is fast-moving and it is still far from guaranteed Twitter will do so.

Twitter is still working on an all-important estimate of its own value, which would need to come in close to Mr. Musk’s offer, and it could also insist on sweeteners such as Mr. Musk agreeing to cover breakup protections should the deal fall apart, some of the people said.

The two sides are meeting Sunday to discuss Mr. Musk’s proposal, the people said.