The French enforcer has been in excellent form this term, but looks set to leave the Parc des Princes with his contract due to expire in six months’ time.
Although a key first-team player, Matuidi is thought to be ready to leave PSG due to the level of competition within the Qatari-backed outfit’s squad.
Manuel Pellegrini sees the 26-year-old as an ideal addition to his ranks, and the sort of player than could make the difference over the remainder of the season as they look to leapfrog Arsenal to claim the Premier League title.
The Chilean already has Yaya Toure and Fernandinho at his disposal, but he is believed to be unconvinced by the ability of backup players such as Jack Rodwell and Javi Garcia.
Manchester United and Chelsea have also been linked with Matuidi, but City are thought to be ready to pay £8m for his signature this week, rather than wait to claim his signature for free at the end of the season.