We present our first attempt to develop a model for soft interactions at high energy, based on the BFKL Pomeron and the CGC/saturation approach. We construct an eikonal-type model, whose opacity is determined by the exchange of the dressed BFKL Pomeron. The Green function of the Pomeron is calculated in the framework of the CGC/saturation approach. Using five parameters we achieve a reasonable description of the experimental data at high energies ((Formula presented.)(Formula presented.) TeV) with overall (Formula presented.) (Formula presented.). The model results in different behavior for the single- and double-diffraction cross sections at high energies. The single-diffraction cross section reaches a saturated value (about 10 mb) at high energies, while the double-diffraction cross section continues growing slowly.