At 15 years of age, the Gunners winger is a Premier League and Champions League player.
Carsley said: “He’s a player that we’re monitoring.
“Sometimes that talent, we have to accelerate it so quickly because of the challenge they are getting at their clubs.
“It’s important that we keep in mind how young Max is and we are fully aware of him. We get all of the feedback from the camps that he plays on and there is definitely time.
“He’ll definitely get his chance within the U21s.”
Carsley has also offered encouragement to Manchester United's 18 year-old winger Shea Lacey.
He added, “He’s been in the pathway a good amount of time now and he’s a player that we rate highly. It worked out well that we needed that position for the training we were doing and Shea was more than happy to come over and train with the Under-21s.
“You can see he’s a good talent. I know he’s struggled with injuries in the past, which has probably held back his development, but I think it’s so important we don’t rush these young players, we let them develop in their own time.
“I think he trained two sessions with us and I enjoyed having him.”