In this work, we analytically investigate the stability of steady-states in a three-dimensional network of ferromagnetic nanowires. We construct a three-dimensional network nanostructure comprising an array of straight nanowires aligned parallel to each other at an equidistance. The analysis is performed within the framework of the Landau-Lifshitz equation. We consider two cases, viz., the network model consists of infinite-length and finite-length nanowires. By employing the classical approach for both cases, we establish sufficient conditions that show that the considered steady-states are exponentially stable. We remark that sufficient conditions depend on the damping and anisotropy coefficients and remain independent of the size of the network and the lengths of the nanowires.