JPMorgan declined to comment for this story. The bank's board has said it opposes the shareholder proposal and that the company's handling of the trading loss shows its current governance works.
The bank's directors are leading an aggressive campaign to persuade shareholders to vote against it, one of the investors said. It is not clear how much investor support there is for the proposal.
The two JPMorgan investors, who were not authorized to speak on the record, said that however the vote shakes out, they plan to continue to push the bank's directors behind the scenes to take at least some power from Dimon.
One investor said they will likely encourage the bank to give more authority to its lead independent director, former ExxonMobil Chief Executive Lee Raymond. At JPMorgan, the lead director is currently known as the "presiding director," a role that includes approving board agendas and schedules and leading meetings of independent directors.
The second investor said they would not be satisfied with anything less than a separation of the two roles because being a chairman is a full-time job.
(Read More: Who Leaked JPMorgan's 'Schemes' Memo?)
Complicating the vote is Dimon's reputation as the best manager on Wall Street. The 57-year-old executive is still viewed by many shareholders as a shrewd leader and they want him to continue to run the bank, albeit with some oversight. Some investors fear that Dimon will leave if he loses the vote.
Dimon's difficulties began last year, when news emerged of the London Whale trades. The bank has since had a series of run-ins with regulators over issues ranging from money laundering controls to allegations of power market manipulation. JPMorgan's growing array of problems has overshadowed last year's record profits in the minds of many investors.
As investors ponder whether Dimon can provide enough oversight to a bank with nearly $2.4 trillion of assets, their doubts could give momentum to an idea held by a small but growing minority of U.S. lawmakers and regulators that the biggest banks are too big to manage.
The vote also comes amid a broader debate in corporate America over whether the head of a company should also lead the directors that oversee the company. In the United Kingdom, the two roles are typically separate.
"Independence is the cornerstone of accountability," said Joe Dear, chief investment officer at the California Public Employees' Retirement System, which owns JPMorgan shares. "As a principle, CalPERS believes boards should be chaired by an independent director, and we support the separation of the CEO and chair roles."
(Read More: Dimon: Controversy Over My Chairman Role a 'Sideshow')
Dear declined to comment specifically on JPMorgan.
The shareholder proposal was sponsored by the American Federation of State, County & Municipal Employees, New York City and state of Connecticut employee retirement plans and the United Kingdom's Hermes Fund Managers.
At last year's meeting, the AFSCME was the sole sponsor of the proposal, and it won 40 percent of investors' votes, relatively high for a measure that the board had opposed.
Last year's vote happened only five days after the company first acknowledged its bad bets on credit derivatives. Since then, shareholders have learned much more about the company's failed risk controls and the trouble it has had with regulators.
(Read More: JPMorgan Investors Propose Splitting CEO, Chairman Roles)
ISS, which is also known as Institutional Shareholder Services, had supported last year's proposal, but this year added a two-page analysis that concluded the London Whale loss had displayed the board's lack of independence from Dimon.
A second proxy advisory firm, Glass, Lewis & Co, endorsed last year's proposal but has yet to announce its recommendation for this year's vote.
Dimon has had other problems recently. U.S. government investigators have found that a JPMorgan unit manipulated trading in the California and Michigan electricity markets, The New York Times reported on Friday.
The Office of the Comptroller of the Currency, one of the bank's main regulators, is also considering censuring the bank for failing to conduct adequate due diligence and report suspicions about Ponzi-schemer Bernard Madoff, Reuters first reported last month.
In his annual letter to shareholders, Dimon said executives throughout the bank are putting other projects on hold or scaling them back, so they can focus on the bank's regulatory obligations. Dozens of these projects are on the back burner now, a source familiar with the situation said.