The 18-year-old midfielder won October's Premier League 2 Player of the Month after impressing at Under-23 level and being rewarded with a UEFA Champions League debut.
He now wants to emulate the success of first-team regular Phil Foden, who is inspiring the next generation with his own journey from City's Academy.
"He's a big inspiration because he's the first one to go through from the Academy," says Palmer. "It gives all of us hope.
"Once you see it, you can kind of believe it, that you can do it and go and be a regular in the first team like he is.
"It's every kid's dream to play for Man City. My ambition is to break through to the first team and score goals. I just have to stay humbled and keep working hard."
Leading by example, well deserved Cole! 🙌🔥 https://t.co/PduCzLcQFT— Man City Academy (@ManCityAcademy) November 16, 2020
Palmer, who has been at the club since playing for the Under-8s, has also been inspired by four-time Premier League champion and his favourite player, David Silva.
"Training with him for a part of last season was really good," says Palmer. "He helped me a lot, like the little things he does. It was good to play with him because I've watched him for a long time.
"The space he finds and he always knows where the opposition players are. Hopefully I can take that off him and learn and bring that into my game.
"He's a club legend at City and he's played there for many years, and played at the highest level like the Champions League. He's won the World Cup. Hopefully, I can follow in his footsteps."