Naughty Dog has already stated that The Last Of Us will not come with co-op integrated into its main campaign, but will the game have a separate co-op mode? Well, with the team recently posting a new ad looking for a 'co-op Game Designer'.
The designer's responsibilities will be...
[C]reating mechanics, game modes, progression systems, reward structures, social features, etc. to serve the co-op experience. Creating and iterating gameplay designs with the team, and working in script to implement and/or tune them.
That sounds a lot like The Last Of Us, but it also sounds like pretty much every AAA game in development right now.
The producer will also be involved in "designing andscripting co-op combat encounters" and "AI behavior design" which seems to fit with the whole 'encounter' system Naughty Dog seems to be crafting for the game.
If I was to hazard a completely out there guess, I would suggest that Naughty Dog is in the process of possibly creating a separate co-op mode in the vein of games like Halo 4, or Resistance 2. Maybe a Left 4 Dead style mode? It could also be a simple mode within the game's multiplayer?
It'd difficult to say at this stage — we can only speculate. Naughty Dog hasn't even shown off multiplayer for The Last Of Us, so we really have no idea what it could possibly look like.