  We report new CHARA/MIRC interferometric observations of the Cepheid
archetype $\delta$ Cep, which aimed at detecting the newly discovered
spectroscopic companion. We reached a maximum dynamic range $\Delta H $ = 6.4,
5.8, and 5.2 mag, respectively within the relative distance to the Cepheid $r <
25$ mas, $25 < r < 50$ mas and $50 < r < 100$ mas. Our observations did not
show strong evidence of a companion. We have a marginal detection at $3\sigma$
with a flux ratio of 0.21\%, but nothing convincing as we found other possible
probable locations. We ruled out the presence of companion with a spectral type
earlier than F0V, A1V and B9V, respectively for the previously cited ranges
$r$. From our estimated sensitivity limits and the Cepheid light curve, we
derived lower-limit magnitudes in the $H$ band for this possible companion to
be $H_\mathrm{comp} > 9.15, 8.31$ and 7.77 mag, respectively for $r < 25$ mas,
$25 < r < 50$ mas and $50 < r < 100$ mas. We also found that to be consistent
with the predicted orbital period, the companion has to be located at a
projected separation $< 24$ mas with a spectral type later than a F0V star.
