According to Calciomercato, City have had a long-term interest in Skriniar and could be prepared to send 32-year-old Aguero to Milan with Gabriel Jesus waiting in the wings to claim the Premier League side's centre forward role.
However, instead of a straight cash deal, Antonio Conte may make an ambitious effort to seal the 'dream' signing of Aguero in the process.
Aguero, who has scored 16 Premier League goals this season, is out of contract next summer and has spoken openly about his desire to finish his career in Argentina.
Inter are on the lookout for a new striker to replace Aguero's international team-mate Lautaro Martinez, who remains one of Barcelona's top transfer targets.
However, it is also reported that the Spanish giants could also complicate a deal for Skriniar to join City as they are said to be interested in a move for the Slovakian defender.
Barca's bitter rivals, Real Madrid, are also said to have asked about the 25-year-old's availability, and even suggested a swap deal involving Achraf Hakimi.
The right back, who has spent the last two years on loan from Real at Borussia Dortmund, is reportedly set to join Inter in a £36.6million deal this week.