Adept operating both as an attacking midfielder and a striker, Wythenhshawe-born Cole has been at City since under-8 level.
He progressed through the Academy age groups to captain the under-18 side in the 2019/20 season, where he was in fine form to lead Gareth Taylor's side to league and cup glory.
Palmer scored 15 times and provided five assists as City were crowned under-18 national champions and hit a brace in the 6-0 victory over Stoke City in the final of the Under-18 Premier League Cup.
His fine form was rewarded when he was invited to train with the first team during the Premier League restart.
The teenager made the bench on four occasions and remained with the squad at the start of the 2020/21 campaign.
Palmer made his first team debut in the Carabao Cup fourth-round tie against Burnley on 30 September 2020.