Alvarez is believed to be a target for Villa, who remain keen to bring in another creative player to support Jack Grealish and Emi Buendia behind last-season's top scorer Ollie Watkins.
Birmingham Live reports in June that Alvarez's agent, Fernando Hidalgo, flew into Europe to hold talks with representatives of clubs interested in his client.
Now, Villa sporting director Johan Lange is set to make a formal offer for the 23-year-old in the next couple of days if claims emerging from South America are to be believed.
TNT Sports are reporting that River are braced for a bid from Villa before the week is out.
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