We present the median surface brightness profiles of diffuse haloes (LAHs) around star-forming galaxies by stacking 155 spectroscopically confirmed emitters (LAEs) at $3<z<4$ in the MUSE Extremely Deep Field (MXDF) with a median luminosity of $ L_ Ly alpha $. After correcting for a systematic surface brightness offset we identified in the data cube, we detect extended emission out to a distance of approx 270 kpc. The median surface-brightness profile shows a power-law decrease in the inner 20 kpc and a possible flattening trend at a greater distance. This shape is similar for LAEs with different luminosities, but the normalisation of the surface-brightness profile increases with luminosity. At distances over 50 kpc, we observe a strong overlap of adjacent LAHs, and the surface brightness is dominated by the LAHs of nearby LAEs. We find no clear evidence of redshift evolution of the observed profiles when comparing with samples at $4<z<5$ and $5<z<6$. Our results are consistent with a scenario in which the inner 20 kpc of the LAH is powered by star formation in the central galaxy, while the LAH beyond a radius of 50 kpc is dominated by photons from surrounding galaxies.