One of the useful generalization of extending notion is FI-extending property. A module is called FI-extending if every fully invariant submodule is essential in a direct summand. In this paper, we explore Weak FI-extending concept by considering only semisimple fully invariant submodules rather than all fully invariant submodules. To this end, we call such a module Weak FI-extending. We obtain that FI-extending modules are properly contained in this new class of modules. Amongst other structural properties, we also deal with direct sums and direct summands of Weak FI-extending modules.