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Maybe. Depends how desperate they are to sell. Have they found somewhere yet? How far off was the offer you're going to decline, that shows a good amount of interest.
We had an offer accepted on one place and they agreed to take it off the market for a month whilst we tried to sell. We couldn't find a buyer so it went back on the market and went to someone else (at a lower price I suspect).
Is there any point making an offer on a house before you accept one on yours?
We have an offer that we are going to decline, no idea if buyer will up there offer to what we want or not.
In the meantime we found a place we really like, in budget.