The Brazilian had a relatively slow start to his third season at Old Trafford, but he's come into form of late with some commanding midfield performances.
"Midfield is the hardest area for our young players to progress because we have some excellent players operating there," said Sir Alex, in his column for United Review.
"But Anderson has certainly cranked up the contest for places after hitting great form. He took his time - he's only 21, remember! - but he has settled and matured."
Sir Alex has a difficult enough task as it is selecting his midfield when everyone is fully fit, and it's even harder to try and contain Anderson's enthusiasm.
"The competition has not dimmed his self-belief, which is important," added the boss. "He has a Brazilian belief in his own ability and he is going to become a top player.
"He is flying at the moment and he certainly wants to play. In fact, he has a face on him like a bag of tripe when I don't play him."