Williams is a genuine threat to Shaw's status at left-back.
But the England international says: "Of course. Brandon's a brilliant player, obviously a very young player.
“There's always room for improvement, for him and for me, and I think it has helped me personally. Before, I had the likes of Youngy to compete for left-back with me, but he switched positions quite a lot.
“Now Brandon has come in as a more specialist left-back and has done really well. Of course, that's made me want to do really well in myself. He's pushed me along.
“It's really good for the boss and the squad to have that kind of competition for places, where we're pushing each other and all improving all the time."