"If you sit down and look at what's happened under (Gottstein's) leadership, I think it's pretty obvious that it has not gone well. And there is no reason why someone like that should sensibly stay in their role," Artisan's Managing Director David Samra said in an interview.
Pressure has been mounting on Gottstein - the last Credit Suisse executive standing after a series of culls - over major scandals and losses racked up during his two year tenure that have hammered its shares and angered investors.
Credit Suisse emphasised Chairman Axel Lehmann's support for Gottstein after a Bloomberg report on Friday about early talks over a potential replacement.
The bank reiterated this on Thursday.
"The chairman clearly endorsed Thomas Gottstein. Nothing has changed in this regard," a spokesperson said.
Artisan - Credit Suisse's ninth biggest shareholder with a 1.5% stake, according to Refinitiv data - said finding the right CEO to turn the bank around was Lehmann's greatest challenge, adding it could take time and Gottstein should only be replaced once a top-notch successor had been found.
Gottstein in late 2020 promised a "clean slate" for the bank after a turbulent first year in office, which began with a spying scandal that cost his predecessor his job and ended with writedowns and litigation.
But troubles only escalated, with a $5.5 billion loss from the unravelling of U.S. investment firm Archegos and the collapse of $10 billion worth of supply chain finance funds in March 2021 prompting management ousters, investigations, and a capital increase - followed by further losses and fresh legal cases.
Other shareholders and investor advisers are unhappy.
"After two years in office, there's been anything but improvement," Karin Landolt, co-managing director at investor advisory firm Actares, said of Gottstein's tenure, which began in February 2020.
However, "a change (of management) for change's sake will not automatically bring Credit Suisse success and restore its good image," Landolt said, adding Actares's key focus was on governance overhaul rather than personnel decisions.
David Herro of Harris Associates, Credit Suisse's third-biggest shareholder according to Refinitiv, told Reuters it was for the board to decide Gottstein's future.
Artisan began building its stake in Credit Suisse following the Archegos investment and Greensill supply chain debacles, and as Antonio Horta-Osorio was brought in as a chairman with a promise to overhaul the bank's culture and strategy.
"When (Horta-Osorio) joined Credit Suisse, and then subsequently a number of issues happened in the share price collapse, we became very interested," Samra said.
But Horta-Osorio left the bank abruptly in January following breaches of COVID-19 quarantine rules.
Samra said the bank should be given two or three years to execute Horta-Osorio's strategy, and give a new CEO time to get up and running before considering more drastic measures.
"We believe that with (the right leadership executing) the right strategy, emphasizing the wealth management business, the real underlying value of Credit Suisse can be recognized in the share price," he said.
"(But) if you don't have the right people to run it and you're not making any progress, then I think you need to start thinking about simplifying the organisation," he said.
That could involve selling some units or separately listing them, or seeking a merger with a Swiss or U.S. bank, Samra said.
While he would leave all the current assets in place under the right CEO, Samra said finding that person could be "very, very difficult".
"There are no obvious candidates that we can identify. And we've talked to many executives in the industry. So I think that's Axel's hardest job right now."
(Reporting by Brenna Hughes Neghaiwi and Oliver Hirt; Additional reporting by Simon Jessop; Editing by Mark Potter)
By Oliver Hirt and Brenna Hughes Neghaiwi