The bile fluid contains various lipids that are secreted at the canalicular membrane of hepatocytes. As the secretion mechanism is still a matter of debate and a direct experimental observation of the secretion process is not possible so far, we used a mathematical model to simulate the extraction of the major bile lipids cholesterol, phosphatidylcholine and sphingomyelin from the outer leaflet of the canalicular membrane. Lipid diffusion was modeled as random movement on a triangular lattice governed by next-neighbor interaction energies. Phase separation in liquid-ordered and liquid-disordered domains was modeled by assigning two alternative ordering states to each lipid species and minimization of next-neighbor ordering energies. Parameterization of the model was performed such that experimentally determined diffusion rates and phases in ternary lipid mixtures of model membranes were correctly recapitulated. The model describes the spontaneous formation of nanodomains in the external leaflet of the canalicular membrane in a time window between 0.1 ms to 10 ms at varying lipid proportions. The extraction of lipid patches from the bile salt soluble nanodomain into the bile reproduced observed biliary phospholipid compositions for a physiological membrane composition. Comparing the outcome of model simulations with available experimental observations clearly favors the extraction of tiny membrane patches composed of about 100-400 lipids as the likely mechanism of biliary lipid secretion.