The stability analysis of a porous medium layer saturated by a nanofluid was pioneered by Nield and Kuznetsov in 2009, which substantially inspires numerous intriguing investigations due to its usefulness in understanding the mechanisms underlying the heat transfer enhancement of nanofluids. Their theory employs Buongiorno’s model for nanofluids and Darcy and/or Brinkman models for porous media. However, the Brownian and thermophoretic diffusion coefficients are considered to be constants in the calculation of the diffusive mass flux of nanoparticles, which may generate a discrepancy in the following investigations. The purpose of this paper is to redo the analysis by taking into account the thermophoretic diffusion coefficient's dependence on the volume fraction of nanoparticles. To prevent probable interactions between nanoparticles and the walls of the pores, the investigation is limited to situations with high porosity, and accordingly Brinkman model is adopted rather than Darcy model. Results show that the thermophoresis creates a strong destabilizing effect to overcome the Darcy-Forchheimer drag, resulting in an unconditionally unstable state for a saturated nanofluid layer heated from below. To explore a more in-depth understanding of the instability, the dispersion diagrams of growing disturbances are depicted for various parameters conditions. It is found that the heat capacity plays an insignificant role in the stability and oscillatory mode does not occur for all considered cases.