How do I get this under contract?!

[Eric Telese]

Hi all. I have access to a great off-market single family where I live in Long Island, New York. My neighbors are living in a nursing home now and their relatives have been dealing with cleaning it out and selling it. They know I want it and have said they want me to get it for a good price. 

I have offered to purchase it as is and deal with cleaning the entire place out to take that off of their hands but they want to get it emptied out themselves. They don’t know what the property is worth and have mentioned numbers varying from 200k-400k. Therefore, they want to get the property appraised so that both parties are getting a fair price. 

That being said, I want to get this under contract so i can be sure I will truly get the first option. I think that someone could come along and offer more than I would be willing to pay for it. 

My question is this- how do I put this under contract without an agreed upon purchase price? Can we say price is TBD contingent on future appraisal? At that point price would be discussed and buyer could back out but seller would not be able to entertain any offers up until then or a different stated date?