We present deep MUSE observations of five quasars within the first Gyr of the universe (z greater than or similar to 6), four of which display extended Ly alpha halos. After PSF subtraction, we reveal halos surrounding two quasars for the first time, as well as confirm the presence of two more halos for which tentative detections exist in long-slit spectroscopic observations and narrowband imaging. The four Lya halos presented here are diverse in morphology and size, they each display spatial asymmetry, and none are centered on the position of the quasar. Spectra of the diffuse halos demonstrate that none are dramatically offset in velocity from the systemic redshift of the quasars (Delta v < 200 km s(-1)); however. each halo shows a broad Ly alpha line, with a velocity width similar to 1000 km s(-1). Total Ly alpha luminosities range between similar to 2 x 10(43) and similar to 2 x 10(44) erg s(-1), reaching maximum radial extents of 13-30 pkpc from the quasar positions. We find larger sizes and higher Ly alpha luminosities than previous literature results at this redshift, but find no correlation between the quasar properties and the Ly alpha halo, suggesting that the detected emission is most closely related to the physical properties of the circumgalactic medium.