When you are migrating a site to a new location, you need to install WordPress in the new location. This can be done from within your hosting panel. This ensures that everything is correctly configured perfectly on the destination. We pick up the Database configuration from the install automatically.
If you migrate a site to a new server, there are many reasons for the error you are seeing.
Before we initiate a migration, we double check everything on the destination so that it is setup correctly. If we get an error wherein we are unable to send a request with the URL to the new server, we will throw the above error.
This error is common when the DNS for the site has not been setup to point to the new server. You can override this and use our "Server IP"/"Domain Server" advanced-option fields. This works well in most cases, though if you are migrating to HTTPS version of site, this can still fail. It is because the destination server is not yet configured to connect to server HTTPS version of site.
Alternatively, you can try migrating to HTTP version of the site.