No β migration to a localhost (local server) is not possible.
Why?
The MigrationPro tool can only connect to a website if it is publicly accessible via the Internet. A localhost environment is only available on your personal computer or local network, which prevents the migration system from accessing it.
What You Can Do Instead
If you want to test migration before going live, set up a staging website or a temporary online domain that is accessible online.
Once migration is complete, you can later move your staging site to localhost if needed.