According to City AM, Mr Fink has two weeks to decide whether to take up the post or to remain with BlackRock.
Mr O'Neal stood down from his post following $8.4 billion losses in the sub-prime crisis, but employing Mr Fink could mean that the bank would also have to buy out his stake in BlackRock, worth $400 million, to avoid a conflict of interest.
Considered to be a leading bond manager, Mr Fink is being regarded by many analysts to be the solution to the problems at the bank.
But Mr Fink could be in demand from Citigroup after it severed ties with former chief executive and chairman, Charles Prince.
Jamie Dixon, chairman and chief executive of JPMorgan, is also being targeted by Citigroup as it seeks a replacement for the departed Mr Prince.