The France international is out of contract in 12 months time, and City and Arsenal have both been linked with summer moves.
But Napoli have identified the 26-year-old holding midfielder as the ideal signing to strengthen their midfield for a Champions League push next term.
The report claims City are willing to offer PSG around £10m, although Matuidi will be able to leave for nothing in a years time.
The 2011-12 Premier League champions have been busy in the transfer market already despite not having named a replacement for departed boss Roberto Mancini.
Brazil international Fernandinho has joined from Shakhtar Donetsk while Jesus Navas has agreed a switch from Sevilla.
The club insist they've learned from the mistakes of last summer when they failed to land any of their top transfer targets and were left struggling as the deadline approached.
Matuidi, who has been a long-term target for Arsenal, primarily operates as a deep lying midfielder. And he enjoyed an impressive season for PSG as the Paris-based side won the Ligue 1 title last term.
He joined the team from St Etienne in 2011 and has 12 caps for his country.