  We present the median surface brightness profiles of diffuse Ly$\alpha$
haloes (LAHs) around star-forming galaxies by stacking 155 spectroscopically
confirmed Ly$\alpha$ emitters (LAEs) at 3<z<4 in the MUSE Extremely Deep Field
(MXDF), with median Ly$\alpha$ luminosity $\mathrm{L_{Ly\alpha} \approx
10^{41.1} erg\,s^{-1}}$. After correcting for a systematic surface brightness
offset we identified in the datacube, we detect extended Ly$\alpha$ emission
out to a distance of 270 kpc. The median Ly$\alpha$ surface brightness profile
shows a power-law decrease in the inner 20 kpc, and a possible flattening trend
at larger distance. This shape is similar for LAEs with different Ly$\alpha$
luminosities, but the normalisation of the surface brightness profile increases
with luminosity. At distances over 50 kpc, we observe strong overlap of
adjacent LAHs, and the Ly$\alpha$ surface brightness is dominated by the LAHs
of nearby LAEs. We find no clear evidence of redshift evolution of the observed
Ly$\alpha$ 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.
