We explore the conditions for thermal instability to operate in the mini-spiral region of the Galactic Centre (Sgr A*), where both hot and cold media are known to coexist. The photoionization Cloudy calculations are performed for different physical states of plasma. We neglect the dynamics of the material and concentrate on studying the parameter ranges where thermal instability may operate, taking into account the past history of Sgr A*'s bolometric luminosity. We show that thermal instability does not operate at the present very low level of Sgr A* activity. However, Sgr A* was much more luminous in the past. For the highest luminosity states, the two-phase medium can be created up to 1.4 pc from the centre. Dust grains tend to suppress the instability, but the dust is destroyed in a strong radiation field and hot plasma. Clumpiness is thus induced in the high-activity period, and the cooling/heating timescales are long enough to preserve the past multi-phase structure. The instability enhances the clumpiness of the mini-spiral medium and creates the possibility for episodes of enhanced accretion of cold clumps towards Sgr A*. The mechanism determines the range of masses and sizes of clouds; under the conditions of Sgr A*, the likely values are 1–10² M_⊕ for the cloud's typical mass.