City believe they have seen off competition from AC Milan for the 21-year-old Argentinian with the final details to be ironed out before an agreement is reached. Sources have told ESPN the overall cost of the transfer could be less than £20 million.
It is likely that Alvarez, who has already been capped five times by Argentina, won't move to the Etihad Stadium until next summer at the earliest but sources have told ESPN he would be considered a first-team signing.
Until he is ready to move to England, City will consider loaning him back to River Plate or arranging another loan elsewhere.
Asked about Alvarez following the 1-1 draw with Southampton on Saturday, Pep Guardiola remained tight-lipped.
"I don't have any information from the club, anything," he said.
"Not one word. I don't know anything. I don't have any information about the club."
Alvarez is considered to be one of the best young players in South America and should City get a deal over the line, it would be a coup of the Premier League champions following interest from Milan, Barcelona and Real Madrid.
City remain open to the idea that he could be part of Guardiola's senior squad next season but sources have told ESPN his arrival would not change their plans to sign an established striker in the summer.