  The Transiting Exoplanet Survey Satellite (TESS) is the latest observational
effort to find exoplanets and map bright transient optical phenomena.
Supernovae (SN) are particularly interesting as cosmological standard candles
for cosmological distance measures. The limiting magnitude of TESS strongly
constrains supernova detection to the very nearby Universe ($m \sim$ 19,
$z<0.05$). We explore the possibility that more distant supernovae that are
gravitationally lensed and magnified by a foreground galaxy can be detected by
TESS, an opportunity to measure the time delay between light paths and
constrain the Hubble constant independently.
  We estimate the rate of occurrence of such systems, assuming reasonable
distributions of magnification, host dust attenuation and redshift. There are
approximately 16 type Ia and 43 core-collapse SN (SNcc) expected to be
observable with TESS each year, which translates to 18% and 43% chance of
detection per year, respectively. Monitoring the largest collections of known
strong galaxy-galaxy lenses from Petrillo et al., this translates into 0.6% and
1.3% chances of a SNIa and SNcc per year. The TESS all-sky detection rates are
lower than those of the Zwicky Transient Facility (ZTF) and Vera Rubin
Observatory. However, on the ecliptic poles, TESS performs almost as well as
its all-sky search thanks to its continuous coverage: 2 and 4% chance of an
observed SN (Ia or cc) each year. These rates argue for timely processing of
full-frame TESS imaging to facilitate follow-up and should motivate further
searches for low-redshift lensing system.
