We describe the search for Lyman break galaxies (LBGs) near the submillimeter-bright starburst galaxy HFLS3 at z = 6.34 and a study on the environment of this massive galaxy during the end of reionization. We performed two independent selections of LBGs on images obtained with the Gran Telescopio Canarias (GTC) and the Hubble Space Telescope (HST) by combining nondetections in bands blueward of the Lyman break and color selection. A total of 10 objects fulfilling the LBG selection criteria at z\gt 5.5 were selected over the 4.54 and 55.5 arcmin2 covered by our HST and GTC images, respectively. The photometric redshift, UV luminosity, and star formation rate of these sources were estimated with models of their spectral energy distribution. These z˜ 6 candidates have physical properties and number densities in agreement with previous results. The UV luminosity function at z ˜ 6 and a Voronoi tessellation analysis of this field show no strong evidence for an overdensity of relatively bright objects ({m}{{F}105{{W}}} \lt 25.9) associated with HFLS3. However, the overdensity parameter deduced from this field and the surface density of objects cannot exclude definitively the LBG overdensity hypothesis. Moreover, we identified three faint objects at less than 3″ from HFLS3 with color consistent with those expected for z ˜ 6 galaxies. Deeper data are needed to confirm their redshifts and to study their association with HFLS3 and the galaxy merger that may be responsible for the massive starburst.