He'd be in Leicester signing a contract faster than he could say "f**k Swansea" if they offered him the post.
A relegated team with plenty of money, a talented squad that has underperformed (unless they had a fire sale), and the safety cushion of parachute payments? If relegated, they should be next season's Burnley unless they appoint a manager who completely screws the pooch.
Buy a proven Championship striker to replace Vardy (I'm sure he'd be aware of a talented Dutch striker with a club who will probably have to sell him at a discount) and probably not a lot else would be needed. He likely wouldn't have a better chance to finish above mid-table handed to him ever again and he'd be a fool not to take it.