  We report the detection of a possible gamma-ray counterpart of the accreting
millisecond pulsar SAX J1808.4-3658. The analysis of ~6 years of data from the
Large Area Telescope on board the Fermi Gamma-ray Space Telescope (Fermi-LAT)
within a region of 15deg radius around the position of the pulsar reveals a
point gamma-ray source detected at a significance of ~6 sigma (Test Statistic
TS = 32), with position compatible with that of SAX J1808.4-3658 within 95%
Confidence Level. The energy flux in the energy range between 0.6 GeV and 10
GeV amounts to (2.1 +- 0.5) x 10-12 erg cm-2 s-1 and the spectrum is
well-represented by a power-law function with photon index 2.1 +- 0.1. We
searched for significant variation of the flux at the spin frequency of the
pulsar and for orbital modulation, taking into account the trials due to the
uncertainties in the position, the orbital motion of the pulsar and the
intrinsic evolution of the pulsar spin. No significant deviation from a
constant flux at any time scale was found, preventing a firm identification via
time variability. Nonetheless, the association of the LAT source as the
gamma-ray counterpart of SAX J1808.4-3658 would match the emission expected
from the millisecond pulsar, if it switches on as a rotation-powered source
during X-ray quiescence.
