Simpson spent two seasons playing alongside Maguire at Leicester City.
"He's a good lad, he's a good person," Simpson told MUTV. "I know straightaway the players will respect him and take to him. Especially at the back, he's a calming influence on the ball, which is what United have needed.
"He knows when to step in, pick up the pace, and he knows when to slow it down. He seems like he's grown more with each game as a leader.
"We've seen some of the stuff as well he's been doing off the field as Man United captain to help out with the NHS and lockdown. He helped me out as well with something. He must be so busy but I asked him to help me out and he sent me a video message.
"He's just a good guy and he's clearly respected and I still think there's more to come from him.
"It's a lot to come in and sign for Man United at that price tag in your first season and then be given the captain's armband, maybe halfway through, so second season he'll just kick on.
"Like you said, there's been some good signings and with him in the team and the young players in the squad I think they'll just grow."