Would you accept this offer on your house?
It all depends on the deal. Most of the sellers I work with would not accept this as written in your question. It's just too risky for them unless you are willing to put up a significant amount of option money that is non-refundable if you can't sell your house. They might consider if you have a contract on your home to sell fairly quickly and you can show them the contract and let them research the ability of the buyer of your house to close.
My advice to most buyers with a house to sell is to put yours on the market, get a contract. Once you get a contract ...then go shopping....unless you want and can pay for two houses for some period of time.
Most relocation companies are not open to a home sale contingency.
Getting your home sold will put you in a A+ buyer position. You could put a contingency in your listing agreement that indicates you will sell upon finding suitable housing and provdie you 30 days. Many first time buyers can live with that as long as the negotiations are win/win.
Best of luck!
and write in that offer,
"Contingent upon the Sale of Buyer's Existing House"?
If that is the question, yes you can write it in an Offer.
But don't count on a Seller accepting it.
A Seller that does accept such a contingency will usually want verification that your house is properly Listed for sale at a realistic price.
There will be further time constraints, and possibly you will be offered a First Right of Refusal
("okay, we accept your offer, but we are keeping the house on the market, and if another Buyer comes along,
we will give you 24 or 48 hours to Buy this house, otherwise it goes to the New Buyer").
That is how is USED to be.
In the current Real Estate Market, with rare exceptions, very few Sellers want to take their house off the market.
(When Real Estate Agents see the word "Contingent" in the MLS, they will generally shy away from showing that property).
Best wishes to you,