Bank of New York Mellon Corp
Citing people familiar with the matter, the Journal reported on Sunday that Kelly has been approached more than once about being a potential successor to Kenneth Lewis, who will retire at the end of this year.
Some Bank of America stakeholders and regulators are pushing the board's search committee to look outside the company for the next CEO, but potential candidates have fallen short of the board's hopes or were not interested, the paper reported on its website.
The search committee could also hire an insider, and Bank of America Chief Risk Officer Gregory Curl and small-business banking head Brian Moynihan are the two top candidates in that case, sources told the Journal.
The search committee is not expected to make a decision until the end of this week at the earliest, these sources told the paper.
Spokesmen for Bank of America and BNY Mellon did not immediately return calls seeking comment on the Journal report.
(Reporting by Anupreeta Das; Editing by Bernard Orr)