Recently we have proposed a mechanism for the magnetization and polarization of the vacuum (M. Urban et al., EPJ D, 2013). We have shown that the vacuum permeability and permittivity may originate from the magnetization and the polarization of continuously appearing and disappearing fermion pairs in vacuum. If we simply model the propagation of the photon in vacuum as a series of transient captures within these ephemeral pairs, we can derive a finite photon velocity equal to the velocity of its associated electromagnetic wave. Within this approach, the propagation of a photon is a statistical process at scales much larger than the Planck scale. Therefore we expect its time of flight to fluctuate. We predict time fluctuation of 50 attosecondper square root of meter. We will present current limits obtained from short Gamma Ray Bursts. We will present an experimental setup, currently in development in CELIA, using XUV attosecond pulses, in order to test this prediction.