How do I encrypt data to be decrypted on a linked server? SQL
It's possible to do what you are suggesting. You can't create the same asymmetric key directly using parameters, but you can backup the database containing the asymmetric key and backup the database master key on the data server. Restore them on the Interface server and drop the private key on the data server using ALTER ASYMMETRIC KEY remove private key. That way the data server can only encrypt and the Interface server can decrypt using the same asymmetric key. 

Or, you can create a symmetric key encrypted by the asymmetric key using the same key_source and identity_value on each server and transfer the data in it's encrypted stated, then decrypt it on the Interface server. It does not matter, in the latter case, if the asymmetric keys are different because each protects keys that are identical on each server. If your goal is to encrypt data in transit, then the second one will be easier to recover if there are any issues.