The main progenitor candidate of Type Ia supernovae (SNe Ia) is white dwarfs in binary systems where the companion star is another white dwarf (double degenerate system) or a less evolved non-degenerate star with R* >~ 0.1 Rsun (single degenerate system), but no direct observational evidence exists that tells which progenitor system is more common. Recent studies suggest that the light curve of a supernova shortly after its explosion can be used to set a limit on the progenitor size, R*. Here, we report a high cadence monitoring observation of SN 2015F, a normal SN Ia, in the galaxy NGC 2442 starting about 84 days before the first light time. With our daily cadence data, we catch the emergence of the radioactively powered light curve, but more importantly detect with a > 97.4% confidence a possible dim precursor emission that appears at roughly 1.5 days before the rise of the radioactively powered emission. The signal is consistent with theoretical expectations for a progenitor system involving a companion star with R* = ~0.1 -- 1 Rsun or a prompt explosion of a double degenerate system, but inconsistent with a typically invoked size of white dwarf progenitor of R* ~ 0.01 Rsun. Upper limits on the precursor emission also constrain the progenitor size to be R*