The Times claim the French champions are preparing a bid for Silva and are willing to pay as much as €70m (£59.1m) for the "unsettled" Portuguese star, who still has three years left on his current deal at the Etihad.
Silva has been identified as a top target for PSG this summer and the French club are said to be "confident that he will move to Paris if a fee can be agreed."
Barcelona have also been strongly linked with the midfielder, who has scored 48 goals in 253 games for City since joining the club in a £43.5m move from Monaco in 2017.
But the Catalan club's ongoing financial troubles have hampered their attempts to sign the Portugal international this summer.
An asking price of €80m (£67m) has reportedly been floated by City for Silva, who was one of the club's stand-out players last season.
He scored eight goals and provided three assists to help Pep Guardiola's side claim their fourth Premier League title in five seasons.
In July, French outlet Le Parisien claimed PSG were keen to sign Silva in a swap deal with Brazilian star Neymar heading to the Etihad.
Silva is yet to make a start for City this season as the speculation surrounding his future continues.
Speaking earlier this month, Silva said: "It's a big club, and they don't want players who are not happy at the club.
"They always say to all of us that if you're not happy, you can go. Of course, they are in business and they want the right amount of money for letting us go, but personally it's a relationship with the club that is very respectful."
He added: "They have always been honest with me and I have always been honest with them.
"I will always respect my relationship with Man City, with the fans, with the staff, with my team-mates, so whatever happens happens, and for sure, it will happen in a very respectful way."
PSG have already made a number of signings this summer as new head coach Christophe Galtier looks to stamp his mark on the squad.
After signing Nuno Mendes on a permanent deal from Sporting after his successful loan spell at the club last season, PSG have also brought Vitinha, Hugo Ekitike, Nordi Mukiele and Renato Sanches to the Parc des Princes.
Featured Image Credit: Alamy
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