It might be possible. I found this on it-
Maybe. The 25th Amendment says "no person constitutionally ineligible to the office of President shall be eligible to that of Vice President of the United States," and the 22nd says you can only be elected twice (and if you succeed to the presidency and serve for more than two years, that counts as one of your terms) so the question would come down to the Supreme Court deciding whether "constitutionally ineligible to the office" includes not being "elected to the office more than twice."
A very strict reading would allow it, because the 22nd Amendment only says a person cannot be
elected President more than twice, but does not say that a person cannot
serve more than twice. However, prior to the 25th Amendment, the Constitution did not explicitly spell out that the Vice President
becomes President in the event of something unfortunate occuring, only that the powers of the President devolve upon the Vice President. So if the Supreme Court takes the words exactly as written, then the answer to your question is yes. If they take the (I would say clear) intent of the Amendments, then the answer is no.
If anything happened the key word is elected. As Vice President he could possibly be considered as selected.
I’m thinking there is exploration of a Biden/Obama ticket. Just a gut feeling.
With Obama's two terms, he's not eligible.