  Intensity mapping (IM) with neutral hydrogen is a promising avenue to probe
the large scale structure of the Universe. In this paper, we demonstrate that
using the 64-dish MeerKAT radio telescope as a connected interferometer, it is
possible to make a statistical detection of HI in the post-reionization
Universe. With the MIGHTEE (MeerKAT International GHz Tiered Extragalactic
Exploration) survey project observing in the L-band ($856 < \nu < 1712$ MHz, $z
< 0.66$), we can achieve the required sensitivity to measure the HI IM power
spectrum on quasi-linear scales, which will provide an important
complementarity to the single-dish IM MeerKAT observations. We present a
purpose-built simulation pipeline that emulates the MIGHTEE observations and
forecast the constraints that can be achieved on the HI power spectrum at $z =
0.27$ for $k > 0.3$ $\rm{Mpc}^{-1}$ using the foreground avoidance method. We
present the power spectrum estimates with the current simulation on the COSMOS
field that includes contributions from HI, noise and point source models
constructed from the observed MIGHTEE data. The results from our
\textit{visibility} based pipeline are in qualitative agreement to the already
available MIGHTEE data. This paper demonstrates that MeerKAT can achieve very
high sensitivity to detect HI with the full MIGHTEE survey on quasi-linear
scales (signal-to-noise ratio $> 7$ at $k=0.49$ $\rm{Mpc}^{-1}$) which are
instrumental in probing cosmological quantities such as the spectral index of
fluctuation, constraints on warm dark matter, the quasi-linear redshift space
distortions and the measurement of the HI content of the Universe up to $z\sim
0.5$.
