B737-800 Captain reported an engine malfunction during climb. The crew reduced power on the engine and returned to the departure airport; and landed.

Narrative

Climbing through about FL200 on departure with the copilot flying; the master caution light illuminated along with the left bleed trip off light on the overhead panel. I ran the QRH procedure for bleed trip off light. With light illuminating again after pressing trip reset button we turned off the left pack per the check list. We stopped our climb at FL250 in consideration of only one pack operating. Shortly there after the left engine had a momentary rollback to about 50% but all other engine indications were normal. Around that time we also heard a thumping sound temporarily and presumably from the engine; but unsure of its source. We reduced the power on the left engine and the sound subsided so we decided to run the engine at a reduced power setting while advising ATC and requesting a diversion to the nearest suitable airport which was ZZZ. Flight attendants also heard the noise and called us immediately. Initially I had them standby; then when I could I tasked the flight attendants with preparing for return to ZZZ while monitoring the engine visually as able. We informed dispatch of our diversion and they provided a new release via ACARS. We also requested CFR (Crash Fire Rescue) vehicles to be present upon landing due to being overweight for landing and our mechanical issue. The FO was flying with the autopilot and was responding well so I had her continue with preparing for landing. The left engine remained at low power for our descent. We elected to gradually reduce the speed while descending to expedite our return. Our speed was above normal operating speeds below 10;000 feet. ATC also told us speed was our discretion. I did verify landing distance was acceptable before landing. While on final approach the power was increased on the left engine which seemed to make the thumping sound return. We reduced power on left engine again and the thumping sound went away. We preceded to land with power reduced on left engine; landed uneventfully and cleared the runway. We had fire command inspect the aircraft; then follow us to the gate. We shut down the #1 engine normally while proceeding to the gate. Cause: To my knowledge the only event was exceeding 250 knots below 10;000 feet using Captains authority during [priority handling] to expedite our diversion. The cause being a possible engine or pack mechanical problem. With the unknown cause of the problem we believed getting on the ground quickly and safely was the best course of action.