Motivated by the widespread experimental observations of nematicity in strongly underdoped cuprate superconductors, we investigate the possibility of enhanced nematic fluctuations in the vicinity of a Mott insulator that displays Néel-type antiferromagnetic order. By performing a strong-coupling expansion of an effective model that contains both Cu-d and O-p orbitals on the square lattice, we demonstrate that quadrupolar fluctuations in the p-orbitals inevitably generate a biquadratic coupling between the spins of the d-orbitals. The key point revealed by our classical Monte-Carlo simulations and large-N calculations is that the biquadratic term favors local stripe-like magnetic fluctuations, which result in an enhanced nematic susceptibility that onsets at a temperature scale determined by the effective Heisenberg exchange J. We discuss the impact of this type of nematic order on the magnetic spectrum and outline possible implications on our understanding of nematicity in the cuprates.