B737-400
Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine; Flight Crew Instrument
Aircraft Equipment Problem Less Severe; Flight Deck / Cabin / Aircraft Event Smoke / Fire / Fumes / Odor
Air Traffic Control Provided Assistance; Flight Crew Landed in Emergency Condition
Aircraft
Just prior to top of decent; the First Flight Attendant reported a strong smell/fumes and reported it appeared to be getting worse. We could [smell] some of it in the cockpit also. I immediately notified ATC and requested priority handling and CFR equipment standing by. ATC immediately gave me direct ZZZ. I let the First Officer continue flying while I ran the emergency checklist for fumes and continued contact with the cabin. A strong smell continued all the way until landing. I conferred with the First Officer and flight attendants and they felt there was no reason to evacuate at that point and I agreed. However; I requested the firetrucks to follow us all the way to the gate just in case.
B737-400 Captain reported cabin fumes during cruise and requested priority handling at destination airport.