OptionMonster's PeteNajraian said that Dimon's leadership was inextricable from the banking giant's success.
"If he's gone, I'm gone," he said on CNBC. "I'm out."
Dimon, who serves as chairman and CEO, reportedly said over the weekend that he would likely leave the helm of JPMorgan if the leadership roles were separated.
(Watch Video: JPMorgan's Jamie Dimon Weighs in on Splitting Roles )
Tim Seymour of EmergingMoney.com said that JPMorgan was strong enough to survive the possible departure of Dimon.
"I married JPMorgan," he said. "I don't necessarily marry Jamie Dimon."
Seymour lauded JPM's CEO as a "fantastic financial engineer" and "someone who's been a great poker player in the political game of the evolution of the financial industry."
JPMorgan's share price would likely stabilize in the long term, he added.
"This is the best of the bunch. This is a long-term marriage. It may not be a trade here," Seymour said. "I would be worried about the headline risk here, but I would be taking advantage of that to get married."
StockMonster's Guy Adami said that he would consider dipping into the stock.
"My sense is they have a deep enough bench where the stock will sell off," Adami said, adding that on the selloff, he would consider getting back in.