The winger made his Premier League debut as a 15 year-old this season and has just returned to training after recovering from a pre-Christmas injury.
Rice told The Sun: “He’s incredible. He’s a talent that I’ve not seen at that age.
“I remember it was (then Arsenal U18 coach Jack) Wilshere who first told me about him.
“He said: ‘I’ve got this 14-year-old who’s playing in the Under-18s. You need to watch him’.
“And from that moment on, it was just…you could tell. You know when a footballer’s good and Max for sure has definitely got it.”
Rice added: “I’ve been in that position and I’ve been a young kid in an academy (at West Ham) and trained with the first team when I was 15, 16.
“So I know sometimes it can feel intimidating. It can feel really weird going up to a first-team player and speaking to them.
“I remember myself going up to Mark Noble, Andy Carroll, James Collins, thinking how are they going to take me in?
“So that’s why when I see the younger kids now, I try to give them as much love as possible because I know how they can be feeling.
“They’re all great kids and that’s the good thing about our group here.
“When we go to the gym in the mornings, the academy boys are always there with us and we interact with them.
“It is really good because I don’t think you would get that at a lot of other clubs where 16, 17-year-olds are around the first-team boys.
“So it’s important we take them in and make sure they’re comfortable in this environment.”