The revised requirements could be proposed as early as June, according to the newspaper.
Schwab is among financial firms being swept up in the worst US banking crisis since 2008.
Harris Associates was the biggest shareholder in Credit Suisse for many years.
Banks are scoring big profits on the widening gap between what they charge borrowers and pay to savers.
Credit Suisse is in the midst of a critical strategic review after multiple missteps drove the bank's share price to record lows.
Businesses being targeted for a boutique-style future include the advisory and deal-making teams.
The struggling European lender wants to slash its cost base by an additional $1 billion.
Khan was given the regional leadership role for Europe, the Middle East and Africa at UBS in 2021.
Bank Chairman Antonio Horta-Osorio is leaving after it was revealed he broke Swiss quarantine protocols.
It's the latest European bank to consider changes at the top in an industry beset by sluggish growth.
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