B737-800 flight crew reported fuel quantity discrepancy during departure climb. Diverted and landed uneventfully.

Narrative

On departure on radar vectors to re-intercept ZZZZZ departure; we got an IMBAL (Imbalance) indication on fuel panel. The left tank showed 8.2K; right tank showed 6.7K. Captain (me) was flying and kept control of aircraft. We leveled off at 10000 ft. FO began running IMBAL checklist. As we started the checklist; I confirmed the fuel panel was configured correctly for departure and it was which to me meant the imbalance was happening with a normal fuel panel configuration. The first part of the checklist concerned itself with do we have a fuel leak. None of the indications mentioned in the checklist were indicative of a leak. So; we either had an external leak which we could not see or there was an internal fuel system issue moving fuel where it was unexpected. So; while the FO ran the checklist to try to mitigate the fuel imbalance; I requested radar vectors back to ZZZ. While we were setting up for the return; the left pumps were on and the right pumps were off per the checklist. It did not seem to be fixing the imbalance which was more confusing. We expected the left tank to begin to lose fuel much quicker than it did. I elected to ask for short vectors because that this point; I wasn't sure which pumps were feeding which tanks because the fuel quantities weren't behaving as we expected. I quickly sent an ACARS to dispatch; prepared the cabin for landing; ran after take off; descent and before landing checklists to confirm all systems were set up for landing. Due to the compressed timing; I elected not to run the Nonroutine Landing Checklist. We landed uneventfully under max landing weight on RWY XX. We taxied clear of the runway and had ground personnel look over aircraft for any unusual leakages or liquids coming from our aircraft. When he confirmed there was nothing unusual with our aircraft; we taxied to the gate. Taxi back and shut down were uneventful. The fuel gauges at gate arrival read approximately 8.0K in left tank and 6.1K in right tank. MX (Maintenance) met me at the gate and we discussed. He suspected either a stuck-open transfer valve OR a problem with the totalizers/fuel gauges.