B737-700 First Officer reported problems with the engine driven hydraulic pumps resulting in requesting priority handling and a precautionary landing at destination airport.

Narrative

During the latter part of our climbout from ZZZ; we observed a LOW PRESSURE caution light on the ENG 1 Hydraulic Pump for System A. After checking for and noting full quantity and pressure in System A; we ran the QRH Checklist which consisted of turning the pump off. A little over a half hour later; we noticed decreasing hydraulic quantity in System A; it went as low as 11% (but pressure stayed constant at approximately 3;000 PSI throughout the flight). Shortly thereafter; on the initial descent into ZZZ1; we got a LOW PRESSURE caution for the ENG 2 Hydraulic Pump on System B. We again ran the same QRH procedure and switched off that hydraulic pump. Even though the electric pumps were maintaining full hydraulic pressure; we were concerned that we had a limited amount of time before significant functional degradation of our hydraulic systems began; particularly with the fluid loss on System A. Knowing at that point that we were due to receive the standard long; low-altitude vectors into ZZZ1; we requested priority handling and received priority handling for a long; straight-in approach to Runway XXL at ZZZ1. We configured early and everything went normally concluding in a 40-degree flap landing. After landing we carefully checked that hydraulic pressure was still normal on both sides (it was) and had the responding Fire Crews check for visible external fluid leaks. The responding crews did not notice any leaks/fluid and System A Hydraulic Quantity had stabilized at 20%; so we taxied into the gate.