  Deep-sea archives that include intermediate-lived radioactive
$^{60}\mathrm{Fe}$ particles suggest the occurrence of several recent
supernovae inside the present-day volume of the Local Bubble during the last
$\sim 10$ Myr. The isotope $^{60}\mathrm{Fe}$ is mainly produced in massive
stars and ejected in supernova explosions, which should always result in a
sizeable yield of $^{26}\mathrm{Al}$ from the same objects. $^{60}\mathrm{Fe}$
and $^{26}\mathrm{Al}$ decay with lifetimes of 3.82 and 1.05 Myr, and emit
$\gamma$-rays at 1332 and 1809 keV, respectively. These $\gamma$-rays have been
measured as diffuse glow of the Milky Way, and would also be expected from
inside the Local Bubble as foreground emission. Based on two scenarios, one
employing a geometrical model and the other state-of-the-art hydrodynamics
simulations, we estimate the expected fluxes of the 1332 and 1809 keV
$\gamma$-ray lines, as well as the resulting 511 keV line from positron
annihilation due to the $^{26}\mathrm{Al}$ $\beta^+$-decay. We find fluxes in
the range of $10^{-6}$-$10^{-5}\,\mathrm{ph\,cm^{-2}\,s^{-1}}$ for all three
lines with isotropic contributions of 10-50%. We show that these fluxes are
within reach for the upcoming COSI-SMEX $\gamma$-ray telescope over its nominal
satellite mission duration of 2 yr. Given the Local Bubble models considered,
we conclude that in the case of 10-20 Myr-old superbubbles, the distributions
of $^{60}\mathrm{Fe}$ and $^{26}\mathrm{Al}$ are not co-spatial - an assumption
usually made in $\gamma$-ray data analyses. In fact, this should be taken into
account however when analysing individual nearby targets for their
$^{60}\mathrm{Fe}$ to $^{26}\mathrm{Al}$ flux ratio as this gauges the stellar
evolution models and the age of the superbubbles. A flux ratio measured for the
Local Bubble could further constrain models of $^{60}\mathrm{Fe}$ deposition on
Earth and its moon.
