It's "nonsensical" to split the role of chairman and CEO at JPMorgan Chase when Jamie Dimon has such a strong track record leading the bank, former board member Lawrence Bossidy told CNBC on Thursday.

At next week's JPMorgan annual meeting, the two biggest U.S. proxy advisors, Institutional Investor Services and Glass Lewis, are pushing a nonbinding proposal to separate the chairman and CEO roles held by Dimon.