We show enhanced entanglement in the pseudogap regime of the Hubbard model using the dynamical vertex approximation (DGA). The pseudogap, a partially gapped electronic state, is observed near the superconducting transition in cuprates and nickelates. Leveraging DGA, we compute the quantum variance-a lower bound to the quantum Fisher information from the spin susceptibility directly on the imaginary Matsubara axis, circumventing the need for ill-controlled an- alytical continuation. The results show qualitative agreement with experimental data. Additionally, Ornstein-Zernike fits provide analytical insights.