(Reuters) - Investors including Saudi Arabia's crown prince and a U.S. private-equity firm run by a former Barclays CEO have shown interest in investing $1 billion or more in Credit Suisse's new investment banking unit, the Wall Street Journal reported on Sunday.

Crown Prince Mohammed bin Salman is considering an investment of around $500 million to back the new unit CS First Boston (CSFB) and its CEO-designate Michael Klein, the report said, adding that bank has not yet received a formal proposal from any Saudi entity.

Additional financial backing could come from U.S. investors including former Barclays chief Bob Diamond's Atlas Merchant Capital, the report said, citing people familiar with the matter.

Credit Suisse did not immediately respond to a request for comment.

Seeking to restore vigor to a business that has been languishing, Credit Suisse in October said that it will reshape its investment bank by resurrecting the First Boston brand. The bank tapped board member Klein to lead CSFB.

Saudi National Bank (SNB), controlled by the government of Saudi Arabia, had earlier pledged to invest up to 1.5 billion Swiss francs ($1.60 billion) in Credit Suisse itself for a stake of up to 9.9%, and said it may back the standalone CSFB which will operate as an independent capital markets and advisory bank headquartered in New York.

Credit Suisse's history with the First Boston brand dates to 1978 when the pair linked up to operate in the London bond market. They later merged to create CS First Boston, but a tough period followed after famed bankers departed and the firm ran into regulatory troubles.

Some bankers and investors have expressed scepticism over its ability to regain its past glory in a shrinking market.

($1 = 0.9373 Swiss francs)

(Reporting by Kanjyik Ghosh and Akriti Sharma in Bengaluru; Editing by Cynthia Osterman)