We search for extended Ly \alpha emission around two z > 6 quasars , SDSS J1030+0524 ( z = 6.309 ) and SDSS J1148+5251 ( z = 6.419 ) using WFC3 narrow-band filters on board the Hubble Space Telescope . For each quasar , we collected two deep , narrow-band images , one sampling the Ly \alpha line+continuum at the quasar redshifts and one of the continuum emission redwards of the line . After carefully modeling the Point Spread Function , we find no evidence for extended Ly \alpha emission . These observations set 2- \sigma limits of L ( Ly \alpha , extended ) < 3.2 \times 10 ^ { 44 } erg s ^ { -1 } for J1030+0524 and L ( Ly \alpha , extended ) < 2.5 \times 10 ^ { 44 } erg s ^ { -1 } for J1148+5251 . Given the star formation rates typically inferred from ( rest-frame ) far–infrared measurements of z \sim 6 quasars , these limits are well below the intrinsic bright Ly \alpha emission expected from the recombination of gas photoionized by the quasars or by the star formation in the host galaxies , and point towards significant Ly \alpha suppression or dust attenuation . However , small extinction values have been observed along the line of sight to the nuclei , thus reddening has to be coupled with other mechanisms for Ly \alpha suppression ( e.g. , resonance scattering ) . No Ly \alpha emitting companions are found , down to a 5- \sigma sensitivity of \sim 1 \times 10 ^ { -17 } erg s ^ { -1 } cm ^ { -2 } arcsec ^ { -2 } ( surface brightness ) and \sim 5 \times 10 ^ { -17 } erg s ^ { -1 } cm ^ { -2 } ( assuming point sources ) .