The coordination numbers of square-well pure and mixture fluids describe the local composition and microstructure of the molecular systems. Coordination number models are therefore used for developing equations of state of square-well fluids. We have proposed new models that originate from the analysis of boundary conditions at low and high densities. The close-packed spherical particle theory is resorted to establish the close-packing boundary condition for different sized square-well mixtures at high densities. For testing the new models, the Monte Carlo simulation has been conducted for the square-well binary mixtures with size ratio up to 3.0 and at high reduced density 1.0. A comprehensive comparison indicates that the new models are superior to the existing models (Lee & Sandler, 1987, Fluid Phase Equlibria 34, 113-147; Lee & Chao, 1987, Molecular Physics 61, 1431-1442, Guo, Wang & Lu, 1990a, Third Phase Equilibria 60, 37-45; Yu & Chen, 1995, Fluid Phase Equilibria 111, 37-51) in the description of the coordination numbers and internal energies of the square-well mixture fluids at high densities. As a result, the new coordination number models proposed can be used for developing equations of state, which is addressed in our sequential article.