Positronium (Ps) formation processes in collisions between positrons and alkali atoms (Li, Na, K, Rb and Cs) in Debye plasma environments have been investigated using the classical trajectory Monte Carlo (CTMC) method for the energy range 1-500 keV. Interactions between the active electron in an alkali atom with the positron have been described using a model potential along with the Debye-Hückel potential. In such a process, positronium formation cross sections have been calculated in unscreened, as well as in Debye plasma, conditions. The results show that the cross sections for positronium formation are significantly affected by Debye screening lengths. Also, positronium formation depends on collision energy and plasma conditions. The effect of Debye plasma environments on such a formation process is explained in terms of the classical trajectory framework.