Jamie Dimon—It's Not all About You: Pension Advisor

A British pension fund advisor—joining calls for JPMorgan Chase to split the role of chairman and CEO—told CNBC on Monday its decision is unaffected by the threat of a possible Jamie Dimon departure.

The Wall Street Journal reported over the weekend that Dimon said in a private meeting at company headquarters last week that he'd consider leaving if he was stripped of the chairman role.

Tim Bush of U.K.-based Pension & Investment Research Consultants—known as PIRC—said in a "Squawk Box" interview, "I'd be surprised if somebody stepped down purely because of splitting the role." He added, "I just would question whether there's another reason and this happens to be something coincidentally happening at the same time."

The two biggest U.S. proxy advisors, Institutional Investor Services and Glass Lewis, are leading the charge to persuade JPMorgan shareholders at next week's annual meeting to vote to appoint an independent board chairman and some new directors. ISS and Glass Lewis have said that last year's more than $6 billion worth of "London Whale" trading losses raise questions about oversight.

But for PIRC, this is "clearly not a referendum" on Dimon, said Bush, chief of governance and financial analysis at the advisory firm. "JPMorgan is one of the most competently run banks in the world," he contended, saying it's a matter of principle because it's unlikely that someone of Dimon's caliber would always be in those positions.

There could also be a conflict, Bush explained.

"If you have a lack of confidence in the chief executive, the chairman should either be able to be there as an effectively unconditional independent support," he continued, and "if necessary, it's the chairman that has the conversation with the chief executive."

By CNBC's Matthew J. Belvedere. Follow him on Twitter @Matt_SquawkCNBC.