Credit Suisse started in recent weeks to speak to shareholders about the move, the people said. Various scenarios are under discussion for the investment bank, including the most drastic option of exiting the U.S. market, two sources said.
No decisions have been made, they added.
The sources did not say how much cash the bank would seek to raise.
A Credit Suisse spokesperson said: "We have said we will update on progress on our comprehensive strategy review when we announce our third-quarter earnings. It would be premature to comment on any potential outcomes before then."
Under restructuring launched under Chairman Axel Lehmann, and previously outlined, the bank envisions shrinking its investment bank to focus even more on its flagship wealth management franchise.
Quarterly results are due on Oct. 27.
Deutsche Bank analysts in August estimated a capital shortfall of at least 4 billion francs, corresponding to about a third of the group's market value.
(Writing by Michael Shields and John O'Donnell; Editing by Elisa Martinuzzi and Edmund Blair)
By Oliver Hirt