NEW YORK—American International Group Inc. is at a point in its recovery where the insurer's next CEO could focus on running day-to-day operations rather than crisis management, observers say.

The issue arose last week when AIG disclosed that President and CEO Robert H. Benmosche is suffering from an undisclosed form of cancer and is undergoing “aggressive chemotherapy.”

In a statement, Mr. Benmosche said he feels fine and continues to follow his normal schedule. Later in the week, AIG's board said Chairman Steve Miller would step in as interim CEO should Mr. Benmosche step down.

But that leaves the question of who would be a permanent replacement should Mr. Benmosche leave.

There are several likely internal candidates, although observers said AIG could seek an outsider with extensive capital management experience.

Mr. Benmosche, the fourth CEO to succeed former Chairman and CEO Maurice R. Greenberg since 2005, is widely credited with doing an effective job of reorganizing the insurer and positioning it for its ultimate independence from the federal government, which bailed out AIG in September 2008.

Mr. Benmosche's success means AIG may no longer need a crisis manager, many observers said.

“The task might be easier today given the excellent job that (Mr. Benmosche) has done,” said John Wicher, principal with John Wicher & Associates Inc. in San Francisco.

“You still need a great leader” but “I don't think you necessarily need someone who has crisis management in his or her resume,” he said.

However, Cathy Seifert, an equity analyst with Standard & Poor's Corp. in New York, said a successor still would need to be someone who is capable of developing a savvy capital market strategy, with the federal government planning ultimately to monetize its AIG stake, as well as have knowledge of the business in order to “rebuild the insurance franchise.”

Possible internal candidates cited by analysts include Peter D. Hancock, executive vp of finance, risk and investments; Chartis Inc. Executive Vp Kristian P. Moor; Jay Wintrob, executive vp of AIG's U.S. life and retirement services; and Thomas Russo, executive vp of legal compliance, regulatory affairs and government affairs and general counsel.

“Someone who knows the company well” and has been through its stabilization period might be a better candidate than an outsider, said Mark Purowitz, a partner with Diamond Management & Technology Consultants Inc. in New York.

Stewart Johnson, a portfolio manager with Stamford, Conn.-based Philo Smith & Co., said an outsider needs international, insurance experience, and good relationships with regulators. “That kind of sums up why I think there's pretty big shoes to fill. There aren't a lot of people” who can fill them, he said. “You need someone of (former General Electric Co. leader Jack Welch's) caliber,” he said.