Goal revealed in early February that the 20-year-old has emerged as a top target for the reigning Serie A champions and that a €30 million (£26m/$34m) agreement is close.
If that move goes through, then the highly-rated Argentine will link up with the Bianconeri over the summer.
He told Corriere dello Sport of his future ambition: “I’ve always wanted to become a professional football player and I’ve made it happen.
“Now I dream of playing in the Champions League for one of the four most important clubs in the world: Juventus, Real Madrid, Barcelona or Manchester United.
“After that, I want to be part of the Argentine national team, even if I know it’s difficult because there’s [Nicolas] Otamendi, one of the best in the world.
“Have Juve already secured me? I don’t know. I don’t deal with the market and my first thought is Genoa.
“There’s still so many matches remaining and I want to keep playing like I am. After that, I’ll talk to the directors and my agent.”
Romero only joined Genoa from Belgrano in the summer of 2018 and has enjoyed a meteoric rise to prominence.
He was handed his debut against Juventus, in a fixture which pitched him into direct competition with five-time Ballon d’Or winner Cristiano Ronaldo.
That challenge was taken in his stride before opening his goal account and being sent off in his next outing against Udinese.
With seven bookings and a red card to his name this season, the combative centre-half has shown that he has the stomach for a fight in any of the top divisions across Europe.
He added when asked about facing Ronaldo and the most fearsome attacking threats in Serie A: “So many people have asked me this question but I have a quiet character and, when I play, I don’t think about who I have in front of me.
“Ronaldo‘s one of the best in the world, [Paulo] Dybala is also very good and Juventus is a great team, but I’m only focused on giving my best.
“[Torino striker Andrea] Belotti is the one who has bothered me the most: he moves a lot and is strong physically.”