Lewis, who only turned 18 last month, made his first team debut in August after skippering the Under-18s to Premier League glory last season.
Since then, he has become the youngest player ever to score on his first Champions League start after he netted against Sevilla.
Gallery | Chairman visits training in Abu Dhabi
Speaking in Abu Dhabi during this week’s training camp, Palmer said: “I always tell him so he knows how good I think he is. Now he’s just got to work hard and I’m sure he’ll get to the top.”
For Lewis, the example set by 20-year-old Palmer and 22-year-old Phil Foden has proved pivotal.
All three are from Greater Manchester and signed for the Club at a young age before progressing through the entire academy structure.
Seeing Palmer and Foden make the grade before him has been a huge help to the full-back.
“I saw them come through when I was younger,” he said.
“Phil did it first and that gave me hope that there was a chance. Then Cole did similar not too long later, it makes you feel like there’s an increased chance of you being able to do it.
“It’s very important that people come before you because then you see that with enough talent and hard work you can do it yourself.”
Click on the above video to hear where Cole and Rico they see their careers right now…