A virus is a tiny organism and may lead to mild-severe illnesses in animals or plants or humans.
Biologically we can term virus as a bit of RNA or DNA in a protein coat. It cannot replicate without another organism.
If we use an image of indicator, we may say yes virus is living. This is because the virus particle is non-cellular but has an NDA core.This core is enclosed in a protein coat and it has spike-like projections in all over its surface.