City have no interest in letting the 22-year-old leave on loan again despite being approached by five European clubs. Alvarez was signed by City in January before being loaned back to River Plate.
Transfer expert Fabrizio Romano reports the aforementioned group includes Premier League sides.
It's not the first time City have knocked back interest in Alvarez.
City chief executive Ferran Soriano revealed the club had rejected offers from several clubs already in May.
That's because the Etihad giants plan to build a new attack led by Alvarez and Erling Haaland next season.