Twitter Inc. is re-examining Elon Musk’s $43 billion takeover offer after the billionaire lined up financing for the bid, in a sign the social-media company could be more receptive to a deal.

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.