Frage nach one would think that it would be
Anfrage nach. I can't tell you if it's completely incorrect, since historically, it wouldn't have been used this way in the first place. (It would have been something like
anfragen bei jemandem + relative clause)
Still, I wouldn't recommend nach, because (following my intuition) the two prepositions, an and nach, don't quite fit together.
Anfragen in connection with some noun usually comes with wegen:
Wegen dem Angebot anfragen
Wegen des Angebots anfragen
Note however, that this is not asking for some offer, but about it. Also consider simply using Anfrage, if it's clear from context what the Anfrage is about.