I've heard the rumor on liberal talk radio, read it online, and even heard it discussed in conversations. Today we know it's not going to happen. Via TPM:

We asked Bill Clinton spokesperson Matt McKenna for a response to the speculation that Bill is eying a takeover of Hillary's Senate seat, now that she's set to become Obama's Secretary of State.

McKenna emailed over this:

"It's completely false. President Clinton is excited to expand the work of his foundation which has more than 1,000 staff and volunteers in 44 countries advancing projects on HIV/AIDS, climate change, sustainable economic development, and childhood obesity."

It's hard to count the barrel of reasons why WJC wouldn't fit well in the Senate. He's overqualified? His scope of expertise and interest is much broader than the smaller-scale state-level attention a good Senator provides?  He'd be bored? The concept of Clinton replacing Clinton as New York's junior Senator is certainly a Sorkin/West Wing-like fun idea, but that really doesn't make it a good one. President Clinton is a valuable asset to America's international goodwill. Let's let Governor Paterson appoint someone who makes sense.

Like Jon Stewart.