Rashford, 27, hasn't played since December 12 and recently expressed his desire for a new challenge.
Manager Ruben Amorim has excluded him from the squad for all but one game since then.
Scholes told Sky Bet's The Overlap: “I think Marcus has let a lot of people down with his attitude and I think that's what the manager is trying to say.
"You think of the young players coming through the team and think of (Alejandro) Garnacho.
"They're looking up to people like Marcus now and he's 27, he's clearly not training properly, he's not living his life properly. They're the examples these people should look at.
"I remember years ago when I told the manager (Ferguson) I didn't want to play in that Arsenal cup game.
"The meeting we had afterward, I thought I was going to get a right b********g here, he said to me, 'The worst thing you did was let your teammates down'. And that really stuck with me.
"Because I wasn't really thinking about that and now I think Marcus Rashford is doing exactly the same.
"Ok, he's not refusing to play, but in the way he is behaving and the way he's training…
"In a way, he's saying he doesn't want to be involved with the team and the fact of letting his teammates down, he should be banished from the dressing room.
"If he’s in and around that and young people are seeing that as an example, the sooner he’s gone the better.”