B737 Captain reported during approach and selecting flaps to one position; the LE Flap Transit Light remained illuminated. The flight crew continued the approach and landed.

Narrative

On downwind; the First Officer asked for flaps 1 while slowing down. Captain (Pilot Monitoring) set the flap handle to Flaps 1 position. After a bit of delay; noticed the LE Flap Transit Light remained illuminated. I handed the radios to the First Officer and began running the LE FLAP TRANSIT light QRH. One LE Flap indicator in the overhead panel was illuminated as well.While running the checklist; I noticed both light had extinguished after about 1 minute into checklist. We elected to land Flaps 15 as per the checklist and ran performance numbers to land on [Runway] XL in ZZZ. I [requested priority handling] with ATC; spoke to the FA's (Flight Attendants); made a PA and sent an ACARS to Dispatch indicating we had [requested priority handling]. We told ATC to inspect our brakes after landing in the event of a higher than normal approach speed. We landed without incident; CFR (Crash Fire Rescue) inspected our brakes and we taxiing back to the gate without further incident. At the gate; Maintenance Control was called and maintenance performed an inspection on system and could not find any fault.