Former President George Bush has worked with Clinton to raise money for victims of the Asian tsunami and the hurricane disaster along the U.S. Gulf Coast.

Asked about his father and Clinton, Bush quipped, "Yes, he and my new brother."

"That's a good relationship. It's a fun relationship to watch," Bush said in an interview with CBS News broadcast on Sunday.

While attending Pope John Paul's funeral, Bush said, "It was fun to see the interplay between dad and Clinton. One of these days, I'll be a member of the ex-president's club. ... I'll be looking for something to do."

He said ex-presidents share rare experiences that others cannot understand. "And so I can understand why ex-presidents are able to put aside old differences," he said.

Bush said he checked in with Clinton occasionally.

"And you know, he says things that makes it obvious -- that makes it obvious to me that we're kind of, you know, on the same wavelength about the job of the presidency. Makes sense, after all, there's this kind of commonality," he said.

Bush jokingly referred to speculation that Sen. Hillary Rodham Clinton, the former president's wife, will seek the Democratic nomination for the presidency. He had earlier referred to the former first lady as "formidable."

"Bush, Clinton, Bush, Clinton," he said, referring to how Bill Clinton had followed his father, and Hillary Clinton could follow him.