B737 First Officer reported a left engine roll back at cruise. The flight crew attempted to adjust the engine thrust; but the engine continued to roll back and failed. The Flight Crew requested priority handling and diverted to make a precautionary landing.

Narrative

We were in cruise flight from ZZZ - ZZZ1. We leveled off at FL340. Shortly after we leveled off we noticed the aircraft yawing a bit. I noticed the right thrust lever advancing and the left one staying in place but the N1 was slowly rolling back. I pushed the left thrust lever up but was unresponsive and the engine continued to roll back and eventually failed. We requested priority handling; ran the engine failure and drift down checklist so we can descend to FL240 which is the top of the relight envelope. While the aircraft was stabilized we attempted a cross bleed restart. Everything appeared to be normal but we never got it to restart. While doing this we determined our best course of action was to divert to ZZZZ. We knew another airline has support there. ACARS communication was very intermittent but we got messages through to Dispatch as to our plans. We continued on to a fix on the ILS XX approach into ZZZZ. Even though I was the Pilot Flying; the Captain had just completed recurrent training the week before so he decided he would perform the landing. I reviewed all the checklists and we continued. The approach was flown flap 15 single engine. We landed uneventfully and taxied off of the Runway to the Gate we were assigned. The Captain made appropriate phone calls to the Chief Pilot; Maintenance and Crew Desk. Overall I think everything was handled well by everyone involved.