Saudi Arabia’s crown prince and a U.S. private-equity firm run by Barclays PLC’s former chief executive are among investors preparing to invest $1 billion or more into Credit Suisse’s new investment bank, people familiar with the matter said.

Crown Prince Mohammed bin Salman is considering an investment of around $500 million to back the new unit, CS First Boston, and its CEO-designate, Michael Klein, some of the people said. Additional financial backing could come from U.S. investors including veteran banker Bob Diamond ‘s Atlas Merchant Capital, people familiar with that potential investment said. Credit Suisse previously said it had $500 million committed from an additional investor it hasn’t named.  

Credit Suisse has received a number of proposals from investors interested in CS First Boston. Credit Suisse Chairman Axel Lehmann at a conference on Thursday said it has other firm commitments in addition to the $500 million from the unnamed investor. The bank hasn’t received a formal proposal from any Saudi entity, some of the people familiar with the matter said. 

Credit Suisse is spinning off the New York-based investment bank as part of a fresh start after being buffeted by scandals, regulatory scrutiny and steep losses. It is raising $4.2 billion in new stock that separately will make Saudi National Bank its largest shareholder. It isn’t clear if Prince Mohammed would make the investment through that bank, or another investment vehicle. He is chairman of the country’s sovereign-wealth fund, Public Investment Fund, which along with another government fund is Saudi National Bank’s main owner. 

Credit Suisse’s stock scraped lows in recent days from the new share sale and a warning from the bank that customers pulled $88.3 billion in investments and deposits. The stock rebounded 9% Friday following comments by Mr. Lehmann that the outflows largely stopped.

Separating CS First Boston would give it a clean balance sheet and move it beyond Credit Suisse’s wider losses and thorny legal issues. Many of its bankers defected to rivals this year. Those staying are being promised a share of profits through a partnership model. The name revives the First Boston brand that made Credit Suisse a force on Wall Street after expanding beyond Switzerland in the 1970s, with Mr. Diamond among its alumni. Analysts say the separation could be lengthy and complex. 

Mr. Klein is to lead the new firm after a career as one of the world’s most sought after deal makers for companies and investors. As a Credit Suisse board member since 2018, he led a review of the investment bank’s strategy over the summer, then got tapped by the bank’s other board members to run the spinoff. 

Making CS First Boston independent could take around two years, Mr. Lehmann said Thursday at the FT Global Banking Summit. He said its balance sheet, structure and governance are being discussed with the Federal Reserve. 

Mr. Klein’s involvement opened the door to Prince Mohammed’s potential investment, people familiar with the talks said. Mr. Klein is a trusted adviser in the kingdom from deals such as the 2019 initial public offering of state-owned oil giant Saudi Arabian Oil Co. 

Prince Mohammed has encouraged Saudi investment into businesses as diverse as electric-vehicle manufacturer Lucid Motors Inc., Twitter Inc., Uber Technologies Inc., Citigroup Inc. and the Premier League soccer club Newcastle United, making the kingdom an increasing force in the U.S. and globally.

Saudi National Bank is to become Credit Suisse’s largest shareholder with a 9.9% stake through the $4.2 billion stock sale being completed this week. Chairman Ammar al-Khudairy said the investment would foster deal-making and bring more banking know-how to the country, and that it might invest in CS First Boston too. 

Atlas Merchant’s potential investment was first reported by Global Capital.

The private-equity firm typically forms consortia with other investors to buy stakes in financial companies.

While at Barclays, Mr. Diamond tapped Mr. Klein for advice in taking over U.S. operations of Lehman Brothers, a complex carve-out similar to the one going on at Credit Suisse. An Atlas Merchant operating partner, Tom King. worked with Mr. Klein at Citigroup. 

Write to Justin Baer at justin.baer@wsj.com, Margot Patrick at margot.patrick@wsj.com and Summer Said at summer.said@wsj.com