The Cherenkov Telescope Array (CTA) is the the next generation facility of imaging atmospheric Cherenkov telescopes; two sites will cover both hemispheres. CTA will reach unprecedented sensitivity, energy and angular resolution in very-high-energy gamma-ray astronomy. Each CTA array will include four Large Size Telescopes (LSTs), designed to cover the low-energy range of the CTA sensitivity ($sim$20 GeV to 200 GeV). In the baseline LST design, the focal-plane camera will be instrumented with 265 photodetector clusters; each will include seven photomultiplier tubes (PMTs), with an entrance window of 1.5 inches in diameter. The PMT design is based on mature and reliable technology. Recently, silicon photomultipliers (SiPMs) are emerging as a competitor. Currently, SiPMs have advantages (e.g. lower operating voltage and tolerance to high illumination levels) and disadvantages (e.g. higher capacitance and cross talk rates), but this technology is still young and rapidly evolving. SiPM technology has a strong potential to become superior to the PMT one in terms of photon detection efficiency and price per square mm of detector area. While the advantage of SiPMs has been proven for high-density, small size cameras, it is yet to be demonstrated for large area cameras such as the one of the LST. We are working to develop a SiPM-based module for the LST camera, in view of a possible camera upgrade. We will describe the solutions we are exploring in order to balance a competitive performance with a minimal impact on the overall LST camera design.