Render an object or texture only near camera

My project has the player in a room with 6 walls with a grid-like texture on them. I want these walls to be invisible until the player gets close to them, at which point, only the part of the wall immediately around the player will be visible. Basically, I want the walls to gradually appear as the player approaches them.

I've tried messing with culling distances and LODs, but they just cause the whole wall to appear or disappear at once. I only want a small section of the wall to be visible. Is there any way I can do this?