Robertson, who was born in Scotland but lived in Australia from five-years-old to 12-years-old, has signed a deal this week that will keep him at the English champions until 2023, reports Optus Sport.
The teenage central midfielder is the son of former Socceroo Mark Robertson, and the grandson of Alex Robertson who also played for Australia.
However, the youngster is eligible to play for Peru and England as well as Australia and Scotland - with all four associations said to be chasing his allegiances.
Robertson is represented by former Liverpool and England striker Michael Owen, who he previously described in an interview with The World Game as being "more like a mentor to me than an agent."
“It’s unbelievable having him there," Robertson said.
"We go out for dinner together and speak about life in general. And it’s great to hear about his past experiences in football.
“His advise to me is to just try and develop as much as I can and not worry too much about trying to play for trophies or anything like that at this stage.
“He just wants me to enjoy my football.”
Robertson is coming off the back of an ankle injury and in March he told The World Game he was grateful for the faith City had shown in him.
“Being offered the City contract is great and getting it all sorted and putting pen to paper is the main focus.
“Injuries are hard mentally and physically ... I’m just grateful the club have offered me such a great deal and have shown so much faith in me.
“The first team’s training pitch is right outside my changing room, so whenever they train, say before a Champions League game, you get to watch.
“That’s good because (being out there with them) is where you want to be one day.
“Pep Guardiola comes to watch our games sometimes. We went on tour to Belgium and he came and watched us there.
“He speaks to us a little bit, and it’s good when you see him there, offering us his feedback also.”
Robertson was raised in Sydney, and was playing for the Hakoah Sydney City club before he made his move to Manchester.
However, it was originally United, not City, that he joined upon leaving Australia - only swapping clubs in 2017.
“At Manchester United, I learned to be 'brave' – football is a lot quicker in England," Robertson told Optus.
“I used to take a lot of touches, dribbling, that’s what I did in Australia. They explained how I need to move the ball quicker.”
Robertson could represent Australia at November’s Under-17 FIFA World Cup in Brazil - however, no decision has been made as of yet.