I'm not sure I understand the question, but I can't see why it won't connect to a router which is not itself connected to the Internet. I've used my phone to connect to my router's diagnostic screen when the connection is bad.
Maybe the problem is at the other end. Have you tried rebooting the router? And have you ever connected to this one before - you sometimes get problems where particular devices and router's are difficult to connect anyway.
Also to be precise, does it say "no internet" because it has not connected, or does it explicitly say that the reason it hasn't connected to the router is because the router is not connected to the Internet? Error messages are not always completely clear (in any computer system, speaking with 30 years' experience in a range of systems).
