Shaw has endured a stop-start period at Old Trafford due to injury and being out of favour with Jose Mourinho, with the Portuguese being critical of the left-back's performance against Brighton & Hove Albion on Saturday evening.
Young has refused to discuss reports which have questioned the future of his teammate, but the versatile wideman feels that Shaw can still become one of world's best during his period in the North-West.
The 32-year-old told BBC Radio 5 live: "I am not here to talk about other people and whatnot. Obviously he is a player that wants to do well, I want to see him doing well. It's like all players, you just have to get your head down and work.
"He is a fantastic player. I feel he can be one of the best in the world. As I say, you've just got to work hard."
Shaw has made just 15 appearances for United in all competitions this season.