With the rapid development of low Earth orbit (LEO) constellation satellite networks and on-board processing, in-network content caching becomes feasible, which can further improve the system performance. In order to minimize user terminals content access delay, a novel caching algorithm by optimizing content placement in LEO satellite constellation networks is proposed in this letter. The formulated problem is proved to be NP-complete (NPC) by reducing it to the 2-disjoint set cover problem, which is a known NPC problem. This letter considers the interactions among distributed satellites for making individual content decisions. Then, this letter adopts an exchange-stable matching (ESM) algorithm based on many-to-many matching game with externalities. Simulation results show that the ESM algorithm can improve the system performance in terms of content access delay.