The Premier League club is planning to make a late bid for the France international although Nasser Al-Khelaifi will not entertain offers.
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Al-Khelaifi is in no mood to do business, however, and has warned City that he will target the club's star players should the club make a move for Matuidi.
Asked if he feared an approach from Manuel Pellegrini's side, he commented: "No. Because they know that if they touch one of our players, we will come into conflict with them, and we will also contact their players.
"We respect all clubs. But if a club try to recruit one of our players, they will have to accept the consequences. And what I say is not only for Manchester City, who, from what I know, have not contacted Matuidi."
Al-Khelaifi had earlier played down PSG's interest in Chelsea winger Eden Hazard, while he insisted that the club would never be in a position to sign Lionel Messi from Barcelona.