This paper aims to inspect the nonlocal Erigen’s elasticity model for free vibrations of thermoelastic diffusive sphere in the reference of dual-phase-lag (DPL) model of generalized thermoelasticity. The effect of non-locality and different models of generalized thermoelasticity, i.e. dual-phase-lag (DPL), Lord–Shulman (LS) models and coupled thermoelasticity (CTE) in the presence and absence of diffusion, has been taken under investigation. Due to time harmonic vibrations, the constitutive relations and governing equations are transformed into ordinary differential equations. By applying the stress free thermal boundary conditions, the frequency equation has been taken under investigation for the possible modes of vibrations in compact form. To discover free vibration analysis from frequency equations, the numerical functional iteration technique has been applied for generating numerical data with the assistance of MATLAB software tools. The obtained analytical results have been presented graphically from numerical computations and simulations. The effect of elastic nonlocality on the frequency shift and thermoelastic damping is represented graphically in some cases of interest and analyzed the obtained numerical results. © 2020 Informa UK Limited, trading as Taylor & Francis Group.