Yes. But the seller will almost certainly reject your offer unless your current home is already under contract to another buyer.
After you accept an offer on the home you are currently selling, you can go house hunting and submit an offer on your next home. Don’t forget to make that offer contingent upon the successful closing of your current, under contract, home.
Many sellers will accept an offer with that contingency as long as the sale of your current home is past the Inspection Period.
Whether the seller will accept your contingent offer depends on how attractive the rest of your offer is to the seller, how likely the seller thinks it is that your current home will close successfully, and how much interest the seller has received from other buyers.
A buyer who needs this contingency may not be able to negotiate as hard with a seller. The seller is doubling the risk that the transaction will not close successfully and that can be disastrous for some home sellers. The risk is doubled because a successful closing is not only dependent upon you being able to get your mortgage, but dependent upon your buyers being able to get their mortgage.
I would be happy to help you if you have any questions about such contingencies in your offers. Call me.
I want to be your Realtor!