Having played for Inter Milan's youth side last season, Zaniolo joined Roma as part of the deal last summer that sent Belgian Radja Nainggolan in the other direction.
The towering teenager, who stands at 1.9 metres (6ft 2in) tall, was only supposed to be a squad player for Eusebio Di Francesco but has emerged as one of the breakout stars in a difficult season for the Roma coach.
On Tuesday, he will line up in his sixth Champions League match for Roma as they host Portuguese giants Porto in their last 16, first-leg tie at the Stadio Olimpico.
On Instagram, Zaniolo showed his delight by sharing two photos, one of him as a football-mad child, the other with the Roma jersey, alongside the message: "Always believe in your dreams."
The past five months have been a whirlwind for the player from Massa, rejected by Fiorentina after coming through their youth system.
He is already being compared to club legend Francesco Totti after becoming the youngest Roma player to score his first three senior goals for the club since Totti, aged 18 in 1995.
"He's like Totti, one who speaks little and always wants the ball," said Di Francesco of the youngster.
"Mentally he's in a good place at the moment and I want to make the most of his youthful energy, his desire and determination."
Italy coach Roberto Mancini had already spotted the potential of the versatile midfielder as he rebuilds after the four-time World Cup winners' failure to qualify for Russia 2018.
It was Mancini who gave Zaniolo his first call-up for Italy on September 3 without him having even played a single game in Serie A.
His Roma debut came later on September 19, playing on the biggest stage against European champions Real Madrid, before getting his league start against Frosinone.
"I'm happy that Di Francesco is playing Zaniolo," said Mancini.
"I had followed him in the Under-19 team and I realised that he had uncommon qualities for such a young boy, and he wasn't even a professional player yet.
"With respect to others, he had more physical presence and more quality. I think that the facts have proved I was right.
"Zaniolo is the talent of the future."
'Best yet to come'
Zaniolo's father Igor was also a professional footballer playing as a forward for lower league sides in Italy.
Zaniolo Jr. came through the Fiorentina youth system but was released by the club in 2016, joining then-Serie B side Virtus Entella where he made his professional debut in March 2017.
He was signed by Inter Milan the following July, but did not play any competitive games for the first team before moving to the capital club.
Zaniolo says his father's experience and advice has helped him.
"We talk three or four times a day. He told me that where I am now is just the beginning, and that I don't need to get a big head because you can fall down just as fast as you rise," he said.
"(Roberto) Mancini told me to stay calm, because if I was called up to the senior squad then it was for good reason.
"I'm not thinking about whether I get called up to the Euros. I think only about playing and enjoying myself. The best is yet to come."
Zaniolo has already attracted attention from big clubs including Juventus, Chelsea and Real Madrid, but Roma look set to hold on to the teenage star.
All could depend if he proves decisive over two legs against Porto, where a quarter-final berth could be worth 15 million euros ($17 million) to his club.
Roma director of football Monchi said the important thing was keeping the youngster's feet on the ground.
The club are currently sixth in Serie A, just one point off the Champions League places.
"Zaniolo helps the team a lot, but he's not the only one," said the Spaniard. "He is still growing and needs to be left in peace, because we are talking about him too much."