Calciomercato.com says City are prepared to flex their financial muscle to beat rivals Manchester United to Skriniar.
Quadruple hopefuls City are ready to smash their transfer record to sign the 24-year-old Slovakia international for £85.5m, according to reports in Italy.
Pep Guardiola's City, like bitter rivals Manchester United, need to bolster their defence, with centre-backs Vincent Kompany and Nicolás Otamendi possibly nearing the end of their Etihad Stadium careers.
Kompany, 32, has still to agree a one-year extension to his contract while Otamendi, 31, has struggled to hold down a starting place this season.
And Skriniar has been identified as their top target.