In a word, no. When applying for a variance there is no set requirement that you offer to sell your property to the neighbors. Conversely, if you need a bulk variance as to lot measurements, and a neighbor has vacant land, it would be in your interests to see if such land is available for you to purchase. Even if you fail in that endeavor, the approving Board must consider the fact that you made a good faith attempt to acquire additional land in order to lessen your variance request.
The Land Use Law and the local ordinances cover your situation. You should definitely contact an attorney who handles zoning issues in your locale. Good luck with your quest.