B737 Captain reported an air turn back and precautionary landing caused by an unsafe landing gear indication that could not be cleared.

Narrative

I was conducting right seat training for a new LCA on Aircraft X ZZZ-ZZZ1. The LCA in training was the Flying Pilot. All preflight; push back; taxi and takeoff ops were normal without incident. We departed Runway XXL and began flying the departure profile. The gear was retracted after the positive rate gear up call. The Flying Pilot called for flaps up; after takeoff checklist. While reading the after takeoff checklist; we noticed that the red gear indicator lights were still illuminated. All other indications such as aircraft climb performance and outside sounds suggested that the gear was retracted. We asked ZZZ Center for a level off at 10;000 ft. and remained in the area to address the non-normal. After we identified the issue as a Gear Disagree and stabilized the airplane; I divided up the duties to have the LCA in training remain as the Flying Pilot and take radio number 1 while I read the non normal checklist. The non normal checklist procedure was followed; but the red gear indicator lights remained illuminated. Since we were still in close proximity to ZZZ; I contacted ZZZ Maintenance Control by radio to help us troubleshoot the issue. I knew I could make contact with Maintenance Control quicker than Maintenance at that moment. I also advised the purser of our situation since it was obvious that our flight path had changed. ZZZ Maintenance Control directed us to cycle the manual gear extension door from open to close. ZZZ Maintenance Control also directed us to extend the landing gear and retract the gear. We accomplished those troubleshooting tasks; but the red gear indication lights remained illuminated. We then called ZZZ and established a phone patch with dispatch and conference with Maintenance Control. I briefed Maintenance Control on all troubleshooting measures; and they directed us to check the circuit breakers. All circuit breakers were in. After all troubleshooting efforts were exhausted; I made the final decision to return to ZZZ. We requested priority handling and asked for aircraft fire crash and rescue equipment to meet us upon landing to mitigate the threat of hot brakes after an overweight landing. I advised the purser of our situation and diversion plan and made PA to the passengers. We began to plan for an overweight landing and advised Maintenance. We determined that a landing could be safely made in ZZZ on Runway XXL by utilizing flaps 40 landing data for the slowest approach speed. We transferred aircraft control for the approach briefing; completed the descent checklist; and advised ATC we were ready for the approach. The training LCA flew the ILS approach to XXL and landed without incident. Aircraft fire crash and rescue met us as we exited the Runway and inspected our brakes. After receiving the all clear; we continued our taxi to the Gate. We were met by Maintenance Control personnel and the ZZZ Assistant Chief Pilot as well. We completed our maintenance write ups; briefings to Maintenance Control and crew debrief. I can not say enough about the outstanding and professional job the training LCA Captain XXX; the inflight crew; ZZZ ARTCC and TRACON; ZZZ Maintenance Control; ZZZ Tower and the dispatch displayed while assisting and/or working this flight. It was a Company team effort to maintain the safety of our flight.