B737-800 Captain reported the flap indications and flap handle did not match during approach. The indicated flaps were 15 versus 40 on the handle. The crew continued the approach with flaps 15 and moved the flap level to 15 to match.

Narrative

During approach on ILS XX into ZZZ the FO (First Officer) was flying and calling for configuration changes on schedule per our company profile/standards prior to 1;000 ft. Prior to running 'below the line' on the landing checklist we noticed the flaps indicated 15 while the handle was at 40 and our airspeed was at Flaps 15 Vapp. Upon using my judgement at the time and Captain's authority; we continued the approach at flaps 15. I moved the flap level to the indicated setting and selected flaps 15 Vref in the FMS. A Landing assessment for flaps 15 was completed and we had plenty of runway distance. I mentioned moving the GPWS flap override switch to override but by that time we were passing through 500 ft. and the FO was already hand flying. We never moved the override switch as I didn't want the FO distracted in a critical phase of landing. We landed and exited the runway safely as a nonevent. After landing I asked my FO to cycle the flaps and that appeared to be working normal on the ground. I also cycled the flaps again while waiting for a gate and they worked normally. Not sure what caused this; perhaps a potential malfunction of the flaps.