  A surprisingly large flux of extraterrestrial high-energy neutrinos was
discovered by the IceCube experiment. While the flux of muon neutrinos with
energies $E>100$ TeV is consistent with the extragalactic gamma-ray background
(EBL) determined by Fermi-LAT, the softer component of the cascade neutrino
flux at $E<100$ TeV is larger than expected. Moreover, a gamma-ray excess at
high Galactic latitudes at energies $E>300$ GeV was found in the data of
Fermi-LAT. The gamma-ray excess at TeV energies and the neutrino excess at
$E<100$ TeV may have a common Galactic origin. In this work, we study the
possibility that both excesses are caused by interactions of cosmic rays (CRs)
with energies up to PeV in the wall of the Local Bubble. Source of these CRs
may be a recent nearby source like Vela. We show that such a scenario can
explain the observed CR flux around the knee, while CR interactions in the
bubble wall can generate a substantial fraction of the observed astrophysical
high-energy neutrino flux below $\sim {\rm few} \times 100$ TeV.
