The business is currently held by Interpublic and the review comes at a time when speculation is mounting that Bruce Nelson, Interpublic's senior executive on the account, is set to leave the company.
The Bank of America works with many IPG agencies, including Draft for creative duties and Initiative for media.
The review will come as a severe blow to IPG, which earlier this year lost the General Motors US media account. Despite a statement in which the bank pledged its support for the network, it has issued requests for proposals to other holding companies.
The Bank of America last reviewed its business in 2002, when IPG successfully defended the account.