Context : Aims : High-resolution imaging in several photometric bands can provide color and astrometric information of the wide-orbit component of Cepheid stars . Such measurements are needed to understand the age and evolution of pulsating stars . In addition , binary Cepheids have the potential to provide direct and model-independent distances and masses . Methods : We used the NAOS-CONICA adaptive optics instrument ( NACO ) in the near-infrared to perform a deep search for wide components around the classical Cepheids , Y Oph , FF Aql , X Sgr , W Sgr , and \eta Aql , within a field of view ( FoV ) of 1.7 \arcsec \times 1.7 \arcsec ( 3.4 \arcsec \times 3.4 \arcsec for \eta Aql ) . Results : We were able to reach contrast \Delta H = 5 –8 mag and \Delta K _ { \mathrm { s } } = 4 –7 mag in the radius range r > 0.2 \arcsec , which enabled us to constrain the presence of wide companions . For Y Oph , FF Aql , X Sgr , W Sgr , and \eta Aql at r > 0.2 \arcsec , we ruled out the presence of companions with a spectral type that is earlier than a B7V , A9V , A9V , A1V , and G5V star , respectively . For 0.1 \arcsec < r < 0.2 \arcsec , no companions earlier than O9V , B3V , B4V , B2V , and B2V star , respectively , are detected . A component is detected close to \eta Aql at projected separation \rho = 654.7 \pm 0.9 mas and a position angle PA = 92.8 \pm 0.1 \degr . We estimated its dereddened apparent magnitude to be m _ { H } ^ { 0 } = 9.34 \pm 0.04 and derived a spectral type that ranges between an F1V and F6V star . Additional photometric and astrometric measurements are necessary to better constrain this star and check its physical association to the \eta Aql system . Conclusions :