There should never be a political appointment to the Federal Reserve, J.P. Morgan Chase International chairman Jacob Frenkel told CNBC on Thursday.

"Central bank independence is one of the most important pillars of economic policy that can generate stability, and the absence of it can generate instability," he said in an interview with Sara Eisen on "Closing Bell."

Frenkel was specifically asked about businessman Herman Cain and conservative economist Steven Moore, both picks of President Donald Trump to fill open seats on the Fed's board. Neither have been formally nominated, but both men share Trump's philosophy for the economy and the direction of interest rates, Vice President Mike Pence said in an interview with CNBC on Wednesday.

"Especially in the modern era, with capital markets being so complex, being a Fed governor or being in general a central banker is a profession," Frankel said. "It's not a political prize or medal for somebody who supported somebody else. The stakes are very, very high."