The likes of Manchester United, Barcelona, Real Madrid, Inter Milan, and Bayern Munich are all keen on the award-winning 21-year-old Argentine, who has been in astonishing form in his homeland.
City are yet to tie up the deal, but reports have suggested that they're closing in on an agreement with the talented starlet having a £20million release clause in his contract with River Plate that expires in December this year.
Should he sign, there's a chance that he could be loaned back to the Argentine side in order to continue his meteoric rise to stardom.
So how much do we know about potential replacement Alvarez? talkSPORT.com takes a deeper look…
Julian Alvarez: Profile
The Argentine was almost destined for a path straight to Madrid after starring on trial in the Spanish capital when he was only 11-years-old.
Alvarez scored two goals in five appearances to help LaLiga giants Real win a youth tournament in 2011.
However, he was too young to make the switch permanent as Madrid's policy is to wait until at least 13 before signing foreign talent.
Alvarez's father Gustavo told Goal: "It would be a dream if he could stay. We are a working family.
"I work in a cereal company and my wife Mariana is a kindergarten teacher."
He also had trials with Boca Juniors before he joined the club's rivals River Plate from local side Atletico Calchin in 2016.
Since his arrival in the River first-team, Alvarez has won the Copa Libertadores, Copa Argentina, and Primera Division, among other trophies.
The forward was in Argentina's squad alongside six-time Ballon d'Or winner Lionel Messi for their victorious Copa America campaign last summer.
Alvarez was the Primera Division's top scorer in 2021 with 20 goals in 35 games, while also being named the South American Footballer of the Year.
His contract with River Plate ends in December so the club would want to avoid seeing the starlet - nicknamed 'The Spider' - leave for free in 12 months.
Julian Alvarez: Position
The youngster primarily operates as a forward where he has managed 24 goals and 18 assists in 46 appearances in 2021.
Alvarez became a regular starter in 2020 with manager Marcelo Gallardo utilising him as both a centre-forward and as a second striker.
Yet, he broke into the first-team on the right due to a succession of attacking options at the time including Eintracht Frankfurt star Rafael Santos Borre.
Alvarez was deployed in a similar position for Argentina, appearing as a second-half substitute in the 4-1 win over Bolivia at the Copa America.
Julian Alvarez: What has been said?
River manager Gallardo: "He is a player that coaches love for his quality, for his generosity, and for his playfulness.
"Any coaching staff would love to have him. He's very young and has a long way to go."
A move to City seems like it's written in the stars with Alvarez once admitting he plays with Pep Guardiola's side on FIFA.
"Playing in Europe is most people's dream because of those leagues' quality and what it means to be at those clubs," he told Radio La Red in October 2020.
"But I am taking it easy. Obviously I talk to my agent and my family, but I know I have to stay focused on what I'm doing.
"Later the time will come, through the work I am doing."
Alvarez added: "On the Playstation I play with Barcelona or Manchester City."