We investigate the feasibility of controlling nonlinearity of an optical fiber by changing the polarization of in-coupled light. The proposed fiber structure has a nanostructured core composed of a stack of sub-wavelength stripes made from thermally matched soft glasses with different refractive indices. Numerical simulation results show both strong phase birefringence (of around 10–3) and small effective mode area, which is around 7.5 μm2 at 2000 nm and is weakly dependent on wavelength. Designed structure further shows different nonlinear coefficients for each of the orthogonally polarized guided modes. The fiber has engineered, flat normal dispersion characteristic for both principal polarization axes and its fabrication would concern use of standard, robust and commercially available soft glasses and combination of two technologically proven structured fiber drawing approaches.