Reef-building corals play an important role in marine ecosystems. However, owing to climate change, ocean acidification, and predation by invasive crown-of-thorns starfish, these corals are declining. As marine animals comprise polyps, reproduction by asexual budding is pivotal in scleractinian coral growth. The fibroblast growth factor (FGF) signaling pathway is essential in coral budding morphogenesis. Here, we sequenced the full-length transcriptomes of four common and frequently dominant reef-building corals and screened out the budding-related FGF and FGFR genes. Thereafter, three-dimensional (3D) models of FGF and FGFR proteins as well as FGF-FGFR binding models were reconstructed. Based on our findings, the FGF8-FGFR3 binding models in Pocillopora damicornis, Montipora capricornis, and Acropora muricata are typical receptor tyrosine kinase-signaling pathways that are similar to the Kringelchen (FGFR) in hydra. However, in P. verrucosa, FGF8 is not the FGFR3 ligand, which is found in other hydrozoan animals, and its FGFR3 must be activated by other tyrosine kinase-type ligands. Overall, this study provides background on the potentially budding propagation signaling pathway activated by the applications of biological agents in reef-building coral culture that could aid in the future restoration of coral reefs.