In this paper we extend naturally the scalarization proximal point method to solve multiobjective unconstrained minimization problems, proposed by Apolinario et al.(2016), from Euclidean spaces to Hadamard manifolds for locally Lipschitz and quasiconvex vector objective functions. Moreover, we present a convergence analysis, under some mild assumptions on the multiobjective function, for two inexact variants of the scalarization proximal point algorithm for this kind of functions. In this sense, strong convergence of all the sequences produced by the methods are obtained. Indeed, each accumulation point, of any sequence generated by these algorithm, is a Pareto critical point for the multiobjective function.