NEW YORK (CNNfn) - A push is under way within AOL Time Warner to drop "AOL" from the company's name.

A source familiar with the situation told CNNfn Monday that America Online Chairman and CEO Jon Miller has told parent company Chairman and CEO Dick Parsons that a name change would be beneficial to the Internet service provider.

"Dick Parsons and senior management are considering a name change as a result of the America Online request," an AOL Time Warner (AOL: Research, Estimates) spokeswoman said. "But this will be a decision that will be made in due course with the board."

The move could be considered at a board meeting scheduled for late September.

It's not clear where the board stands, but it's unlikely that the board would oppose a name change if the AOL management was in favor, according to the Wall Street Journal, citing a person familiar with the situation.

Miller's team feels the corporate name is confusing to the public, including America Online members, the source said. The corporate name is often shortened to AOL, which is how America Online, the ISP, has long been nicknamed.

AOL Time Warner is the parent company of CNN, CNNfn and CNN/Money