Host Institution - Marie-Curie individual fellowship
For Marie Curie fellowships you shouldn't already be employed by the host institution. These fellowships are meant to encourage mobility so you must apply to go to some other place.


  could I assign a host Institution and in case that I receive the fellowship, I can then start working on it?


Yes that's exactly the principle. However be careful: you don't just pick a host institution, the key factor in these fellowships is to have a strong research plan prepared in collaboration with the host institution.