Could Bill Clinton Be Vice President If Hillary Clinton Wins

The original Constitution had no requirements for the office of vice president.

However, the 12th Amendment, ratified in 1804, said that, "no person constitutionally ineligible to the office of President shall be eligible to that of Vice-President of the United States."
So that would mean that a vice president would have to meet the requirements to be president laid out in Article II of the Constitution. Principally, the person would have to be born in the United States, be at least 35 years of age and have been a resident of this country for the preceding 14 years. So far, so good. Maybe a former president, like Bill Clinton, could serve as vice president.

Electing Bill as VP for Hillary would be difficult, because they're from the same state.  The Constitution forbids the 538 electors from voting for a President and VP from their own state.  Hillary and Bill are both from New York now, so the 29 electors of New York could either vote for Hillary or Bill but not both.  Needless to say, that is less than optimal.

Now, if someone else were elected VP and either died or resigned, Hillary could appoint Bill to replace them as VP. But the Congress has to approve.  Would they?  It looks like we'll still have a Republican Congress.  

Why would Hillary waste the position on someone who's out of the game, so to speak?  She can win points with her party with that assignment, so wasting it on her husband wouldn't help.