  Hydrogen Ly${\alpha}$ haloes (LAHs) are commonly used as a tracer of the
circumgalactic medium (CGM) at high redshifts. In this work, we aim to explore
the existence of Ly${\alpha}$ haloes around individual UV-selected galaxies,
rather than around Ly${\alpha}$ emitters (LAEs), at high redshifts. Our sample
was continuum-selected with F775W<=27.5, and spectroscopic redshifts were
assigned or constrained for all the sources thanks to the deepest (100- to
140-hour) existing Very Large Telescope (VLT)/Multi-Unit Spectroscopic Explorer
(MUSE) data with adaptive optics. The final sample includes 21 galaxies that
are purely F775W-magnitude selected within the redshift range z=2.9-4.4 and
within a UV magnitude range -20<=M1500<= -18, thus avoiding any bias toward
LAEs. We tested whether galaxy's Ly${\alpha}$ emission is significantly more
extended than the MUSE PSF-convolved continuum component. We find 17 LAHs and
four non-LAHs. We report the first individual detections of extended
Ly${\alpha}$ emission around non-LAEs. The Ly${\alpha}$ halo fraction is thus
as high as $81.0^{+10.3}_{-11.2}$%, which is close to that for LAEs at z=3-6 in
the literature. This implies that UV-selected galaxies generally have a large
amount of hydrogen in their CGM. We derived the mean surface brightness (SB)
profile for our LAHs with cosmic dimming corrections and find that Ly${\alpha}$
emission extends to 5.4 arcsec (~40 physical kpc at the midpoint redshift
z=3.6) above the typical 1${\sigma}$ SB limit. The incidence rate of
surrounding gas detected in Ly${\alpha}$ per one-dimensional line of sight per
unit redshift, dn/dz, is estimated to be $0.76^{+0.09}_{-0.09}$ for galaxies
with M1500<= -18 mag at z~3.7. Assuming that Ly${\alpha}$ emission and
absorption arise in the same gas, this suggests, based on abundance matching,
that LAHs trace the same gas as damped Ly${\alpha}$ systems (DLAs) and
sub-DLAs.
