  Studying the properties of the solar convection using high-resolution
spectropolarimetry began in the early 90's with the focus on observations in
the visible wavelength regions. Its extension to the infrared (IR) remains
largely unexplored. The IR iron lines around 15600\,$\rm{\AA}$, most commonly
known for their high magnetic sensitivity, also have a non-zero response to
line-of-sight velocity below $\log (\tau)=0.0$. In this paper we aim to tap
this potential to explore the possibility of using them to measure sub-surface
convective velocities. By assuming a snapshot of a three-dimensional
magnetohydrodynamic simulation to represent the quiet Sun, we investigate how
well the iron IR lines can reproduce the LOS velocity in the cube and up to
what depth. We use the recently developed spectropolarimetric inversion code
SNAPI and discuss the optimal node placements for the retrieval of reliable
results from these spectral lines. We find that the IR iron lines can measure
the convective velocities down to $\log (\tau)=0.5$, below the photosphere, not
only at original resolution of the cube but also when degraded with a
reasonable spectral and spatial PSF and stray light. Meanwhile, the commonly
used Fe~{\sc i} 6300\,\AA{} line pair performs significantly worse. Our
investigation reveals that the IR iron lines can probe the subsurface
convection in the solar photosphere. This paper is a first step towards
exploiting this diagnostic potential.
