Elon Musk’s team has held talks with investors about raising up to $3 billion to repay some of the $13 billion in debt tacked onto Twitter Inc. as part of his buyout of the company, people familiar with the matter said.

In December, Mr. Musk’s representatives discussed selling up to $3 billion in new Twitter shares, people familiar with the matter said.

Mr. Musk’s team has said to people familiar with the finances of the company that an equity raise, if successful, could be used to pay down an unsecured portion of the debt that carries the highest interest rate within the $13 billion Twitter loan package, people familiar with the matter said.

Paying off the debt would provide welcome financial relief to Twitter, which has struggled to keep advertisers on the platform. In November, Mr. Musk said Twitter had suffered “a massive drop in revenue” and was losing over $4 million a day. He also said that month that bankruptcy was a possibility for the company, although Mr. Musk later shared more upbeat prospects for the company, saying he expects Twitter to be roughly cash-flow break-even in 2023 as he has slashed some 6,000 jobs.

The state of the fundraising talks couldn’t be learned. In mid-December, Mr. Musk’s team reached out to new and existing backers about raising new equity capital at the original Twitter takeover price.

Mr. Musk’s advisers had hoped to reach a deal to raise cash at the initial takeover price by the end of 2022, according to an email sent to prospective investors at the time. However, some prospective backers said they balked at the terms, given concerns about Twitter’s financial performance. The Musk team didn’t specify a funding amount or purpose for the fundraise in the email.

Fidelity, one of the co-investors that backed Mr. Musk’s takeover of Twitter, wrote down its stake in Twitter by 56% in November, public filings show, suggesting Mr. Musk would face an uphill battle raising funds at the original valuation from outside investors. The banks holding the $13 billion in debt that backed his takeover of the company haven’t yet received any formal notice of any repayments, people familiar with the matter said.