That wont work. The rats thought about putting Billy Jeff back in office that way, but...
"The vice-president must be qualified to be President. According to the twelfth amendment of the Constitution, "no person constitutionally ineligible to the office of President shall be eligible to that of Vice-President of the United States.""
Bubba shot his wad, so to speak, with his election to the Presidency.
Bill Clinton is no longer eligible to hold the office of President so he is ineligible to be elected to the Vice-Presidency.
Clinton is NOT constitutionally ineligible.
He is barred FROM BEING ELECTED again.
As far as his constitutional eligibility, he is >35 years old, he was born in Arkansas, and he has had legal US residence for the past 14 years.