  Object 1I/2017 U1 (`Oumuamua) is the first interstellar small body ever
discovered in the solar system. By the time of discovery, it had already passed
perihelion. To investigate the behavior of `Oumuamua around perihelion, we
searched for it in Solar and Heliospheric Observatory (SOHO) and Solar
TErrestrial RElations Observatory (STEREO) images from early 2017 September
(preperihelion), but did not detect it. The nondetection of `Oumuamua by STEREO
renders more stringent constraints on its physical properties thanks to the
extreme forward-scattering observing geometry. Assuming geometric albedo $p_V =
0.1$, the effective scattering cross-section of any dust coma was $\lesssim
\left(2.1 \pm 0.2 \right) \times 10^{4}$ m$^{2}$. Assuming it behaved like a
typical solar-system comet this would correspond to a total mass of $\lesssim
20 \pm 2$ kg, and a water production rate of $\lesssim \left(6.1 \pm 0.5
\right) \times 10^{25}$ s$^{-1}$ at heliocentric distance $r_{\rm H} = 0.375$
au. If scaled to post-discovery $r_{\rm H}$, the water production rate would be
smaller than any of the previously reported upper limits by at least an order
of magnitude. To exhibit the reported nongravitational motion with our default
assumptions requires a nucleus bulk density $\lesssim$40 kg m$^{-3}$; higher
bulk densities are possible for other assumptions. Alternatively, we show that
thermal fracturing could have plausibly removed an inert surface layer between
these observations and discovery, thus initiating activity after `Oumuamua left
the field of view of STEREO.
