Middle-Earth: Shadow of Mordor is a single-player only experience, and so won't feature any form of co-op or multiplayer.
The news comes courtesy of developer Monolith's Twitter account, which also confirmed the game is currently not in development for Wii U.
This is good news. No multiplayer means they can focus their efforts on the story, and gameplay elements. This is one those games that I think will benefit the most without a tact on multiplayer to steal development time. Also, no love for Wii U it seems but that's another story.