I might ask, but I'd say something like "If you are done with that, could I please borrow it?" If they don't want it back, they can say "Sure, keep it, I'm done", and if they don't explicitly say they don't want it back, then I'd give it back when I'm done.
I've had people ask me, and I'm happy to oblige. I've had people look at my stack of magazines and ask, and I've had to explicitly say "You're welcome to read it, but I need it back since I haven't read it yet".
I usually drop the stack of what I read on a seat or table or in the club as I get off the plane in the spirit of reuse beats recycling.