"I think the Fed has shown the right level of caution," Staley told CNBC's "Squawk on the Street" Monday. "They are data dependent. I think what they see in the labor markets and what they see in the underlying economy ... that's what's driving this move up in interest rates."
Staley said, if the Fed should raise rates, he thinks just the opposite of what Trump described would happen.
"If there is a correlation between where interest rates go, economic growth, the labor market ... that should translate also into a pretty good environment for corporations," Staley said.
"I'm not quite sure I'd make that connection that rising interest rates will hurt the equity markets," he added.