If your neighbor is seeking to establish an "easement by necessity," he will have to pay for it, and likely would be required to share in the driveway cost.
If he can't prove some right to use the driveway, such as an "easement by necessity" as noted by another lawyer, your neighbor likely has no claim to use of the easement. "Easement by necessity" typically requires no other access, which does not sound like the case here. You can certainly approach your neighbor and offer to grant him easement rights (if you are so inclined), but at a cost. Not only should your neighbor pay for any easement rights, but you would need to document the agreement and work out other terms, including who has the obligation to maintenance, etc. I would suggest you contact a real estate lawyer in your area.
Posts on this forum are intended for educational and information purposes only and do not create an attorney client relationship. The answers posted should not be treated as legal advice. The posts are intended to be accurate but are based on incomplete information and may be truncated for expediency or to avoid disclosing confidential advice on a public forum. They are not a substitute for speaking directly with an attorney in your area. Mr. Thayer is licensed in Washington state only and laws in your jurisdiction may vary.
There is no guarantee that a court will require maintenance cost sharing from your neighbor. They commonly do in such cases, but not always. If instead of waiting for the court to make a decision you sell your neighbor an easement and reach an agreement about the maintenance costs then you will likely be better off.