The 33-year-old will see his contract with Barcelona expire at the end of this season.
He has been permitted to speak with foreign clubs since January 1.
Due to his incredibly high wages, City and PSG are the only clubs able to afford the Argentinian superstar.
ESPN claims City officials have chosen to remain low-key about their interest in Messi and have secretly been in contact with his representatives for weeks.
The Sky Blues, who are in the drivers seat to win another Premier League title, will not make a formal approach until March or April.
Reports have claimed the Parisians are willing to offer a preposterous contract of £800,000-a-week basic salary in addition to a £40m signing-on fee.
If the reports are true, City would find it extremely hard, if not impossible, to match these terms.