The 12th amendment text suggests he couldn't be VP because he is ineligible to be elected president under the 22nd amendment, and the 12th requires the VP to be eligible to be president. But that's about elections.
He could be appointed to the VP, potentially, but that would mean the Republicans would have to put up a ticket with the intent of the elected VP resigning so the elected President can nominate Trump as his new VP. Then get Congress to confirm Trump, which would require a Republican majority in both houses. The new VP would have to be onboard with this, or not onboard but have so many skeletons in their closet that a resignation can be forced. Which would make them a bad running mate and drag the ticket down.
He could be appointed to the VP, potentially, but that would mean the Republicans would have to put up a ticket with the intent of the elected VP resigning so the elected President can nominate Trump as his new VP. Then get Congress to confirm Trump, which would require a Republican majority in both houses. The new VP would have to be onboard with this, or not onboard but have so many skeletons in their closet that a resignation can be forced. Which would make them a bad running mate and drag the ticket down.