B737-800
Flight Crew Air Transport Pilot (ATP)
Aircraft Equipment Problem Less Severe; Inflight Event / Encounter Fuel Issue
Flight Crew Returned To Departure Airport; Flight Crew Landed As Precaution
Aircraft
In the climb; an amber fuel imbalance was noticed on the fuel quantity indicator. The appropriate checklists where done to determine the source or why the imbalance [occurred]; that was not present before or during takeoff. It was later monitoring the fuel; that we [realized we] might [have] a possible fuel leak. The [projected] fuel at destination [continued to decrease]. The fuel over enroute fixes was also 1;000 lbs less than planned. After a safe landing back [departure airport]; the center fuel tank had approximately 2;300 lbs of fuel and the right center pump low pressure light illuminates; which only illuminates when failure occurs or little or no fuel on the center tank. Aircraft was parked at the gate safely without further events.
B737-800 First Officer reported returning to departure airport after experiencing a fuel imbalance and possible fuel leak.