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Janet Yellen should be replaced as Federal Reserve chair, long-time Wall Street dealmaker Jimmy Dunne said Tuesday.

The senior managing principal and co-founder of Sandler O'Neill told CNBC's "Squawk Box" he hopes a Republican president would choose a different leader of the central bank.

While praising Ben Bernanke for his time as Fed chair, Dunne said Bernanke's successor needed to be someone who was going to "take the foot off the gas."

The financial turmoil of 2016 is threatening to halt further Fed rate hikes. Policymakers increased rates for the first time in more than nine year in December, and projected at the time four more hikes this year.

Interest rates need to go higher, Dunne said. "We've been on an elevator shaft going up for seven years now."

Dunne said his choice for Fed chair would be former central bank governor Kevin Warsh, who was nominated to the Fed board in 2006 by President George W. Bush. Warsh resigned in 2011.

In hoping for a Republican in the White House, Dunne said GOP front-runner Donald Trump is "entertaining" but should be mayor of New York City, not president of the United States. He's be in favor of former New York City Mayor Mike Bloomberg entering the race.

"We can't have [Ted] Cruz," he said. Dunne said he likes Ohio Gov. John Kasich the best, with Sen. Marco Rubio as vice president. Though he sees a Rubio-Kasich ticket as more likely.

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But Dunne doesn't have much confidence in any candidate when it comes to the economy. "The top presidential candidates, there's not somebody that I think, boy they could really understand the economy and do something about it."