  The aim of the paper is to estimate distances to dense molecular cores that
harbour Very Low Luminosity Objects (VeLLO) detected by Spitzer Space Telescope
and to confirm their VeLLO nature. The cloud distances are estimated using
near-IR photometric method. We use a technique that provides spectral
classification of stars lying towards the fields containing the clouds into
main sequence and giants. In this technique, the observed (J-H) and (H-Ks)
colours are dereddened simultaneously using trial values of A_V and a normal
interstellar extinction law. The best fit of the dereddened colours to the
intrinsic colours giving a minimum value of chi^{2} then yields the
corresponding spectral type and A_V for the star. The main sequence stars, thus
classified, are then utilized in an A_V versus distance plot to bracket the
cloud distances. The typical error in the estimation of distances to the clouds
are found to be ~18%.We estimated distances to seven cloud cores, IRAM04191,
L1521F, BHR111, L328, L673-7, L1014, and L1148 using the above method. These
clouds contain VeLLO candidates. The estimated distances to the cores are found
to be 127\pm25 pc (IRAM04191), 136\pm36 pc (L1521F), 355\pm65 pc (BHR111),
217\pm30 pc (L328), 240\pm45 pc (L673-7), 258\pm50 pc (L1014), and 301\pm55 pc
(L1148). We re-evaluated the internal luminosities of the VeLLOs discovered in
these seven clouds using the distances estimated from this work. Except for
L1014-IRS (L_{int}=0.15 L_{\odot}), all other VeLLO candidates are found to be
consistent with the definition of a VeLLO (L_{int}<=0.1L_{\odot}). In addition
to the cores that harbour VeLLO candidates, we also obtained distances to the
clouds L323, L675, L676, CB 188, L1122, L1152, L1155, L1157 and L1158 which are
located in the directions of the above seven cores. Towards L1521F and L1148 we
found evidence of the presence of multiple dust layers.
