Pogba continues to be linked with a move away this summer.
Scholes told MUTV: "There's so much competition for places now but that's all part of being a Manchester United player.
"Once you've got the shirt you have to try and keep it, you have to perform week in, week out and make sure the player – the good player – waiting behind to get a game that you don't allow the manager to pick him because of your performance.
"The future's bright, I think Ole is doing really well, he's got a really good attacking team. You think of the players you've got, Martial, Rashford, Fernandes, Pogba when he's back, McTominay – really good young players – Williams coming into it. I think it's a really exciting time."