Results on K{sup +} and K{sup 0} meson production in {sub 44}{sup 96}Ru + {sub 44}{sup 96}Ru and {sub 40}{sup 96}Zr + {sub 40}{sup 96}Zr collisions at a beam kinetic energy of 1.528A GeV, measured with the FOPI detector at GSI-Darmstadt, are investigated as a possible probe of isospin effects in high-density nuclear matter. The measured double ratio (K{sup +}/K{sup 0}){sub Ru}/(K{sup +}/K{sup 0}){sub Zr} is compared to the predictions of a thermal model and a relativistic mean field transport model using two different collision scenarios and under different assumptions on the stiffness of the symmetry energy. We find good agreement with the thermal model prediction and the assumption of a soft symmetry energy for infinite nuclear matter, while more realistic transport simulations of the collisions show a similar agreement with the data but also exhibit a reduced sensitivity to the symmetry term.