Studying the properties of the solar convection using high-resolution spectropolarimetry began in the early 90s 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.
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