A person familiar with Mr. Geithner’s thinking who was not authorized to speak publicly said that there was “no secret handshake” between the New York Fed and Goldman, describing such speculation as a conspiracy theory.

Furthermore, others say, it makes sense that Goldman would have a presence in organizations like the New York Fed.

“This is a very small, close-knit world. The fact that all of the major financial services firms, investment banking firms are in New York City means that when work is to be done, you’re going to be dealing with one of these guys,” said Mr. Langevoort at Georgetown. “The work of selecting the head of the New York Fed or a blue-ribbon commission  any of that sort of work  is going to involve a standard cast of characters.”

Being inside may not curry special favor anyway, some people note. Even though Mr. Fuld served on the board of the New York Fed, his proximity to federal power didn’t spare Lehman from bankruptcy.

But when bankruptcy loomed for A.I.G.  a collapse regulators feared would take down the entire financial system  federal officials found themselves once again turning to someone who had a Goldman connection. Once the government decided to grant A.I.G., the largest insurance company, an $85 billion lifeline (which has since grown to about $122 billion) to prevent a collapse, regulators, including Mr. Paulson and Mr. Geithner, wanted new executive blood at the top.

They picked Edward M. Liddy, the former C.E.O. of the insurer Allstate. Mr. Liddy had been a Goldman director since 2003  he resigned after taking the A.I.G. job  and was chairman of the audit committee. (Another former Goldman executive, Suzanne Nora Johnson, was named to the A.I.G. board this summer.)

Like many Wall Street firms, Goldman also had financial ties to A.I.G. It was the insurer’s largest trading partner, with exposure to $20 billion in credit derivatives, and could have faced losses had A.I.G. collapsed. Goldman has said repeatedly that its exposure to A.I.G. was “immaterial” and that the $20 billion was hedged so completely that it would have insulated the firm from significant losses.