  Theoretical models predict that the compressed interstellar medium around
runaway O stars can produce high-energy non-thermal diffuse emission, in
particular, non-thermal X-ray and $\gamma$-ray emission. So far, detection of
non-thermal X-ray emission was claimed for only one runaway star AE Aur. We
present a search for non-thermal diffuse X-ray emission from bow shocks using
archived XMM-Newton observations for a clean sample of 6 well-determined
runaway O stars. We find that none of these objects present diffuse X-ray
emission associated to their bow shocks, similarly to previous X-ray studies
toward $\zeta$ Oph and BD$+$43$^{\circ}$3654. We carefully investigated
multi-wavelength observations of AE Aur and could not confirm previous findings
of non-thermal X-rays. We conclude that so far there is no clear evidence of
non-thermal extended emission in bow shocks around runaway O stars.
