According to the reports, the police prefecture has asked the French Professional Football League (LFP) to reschedule the fixture, which is due to be played in Paris on Sunday.
Sports daily L'Equipe reported that the match could be moved to Monday, although no official decision has been announced.
French officials will mount a "massive" security operation for protests planned on Saturday, with troops reinforcing police, Prime Minister Sebastien Lecornu said on Tuesday, after rioting and looting swept through Paris and other French cities on October 17.
The PSG-Lyon game is among several high-profile sporting events scheduled in the French capital area this weekend.
The Pittsburgh Steelers are due to face the New Orleans Saints in an NFL regular-season game at the Stade de France on Sunday, an event expected to require a significant police deployment.
Separately, Toulouse's Ligue 1 home match against Troyes has already been pushed back from Saturday to Sunday at the request of local authorities, the LFP said on Wednesday.
The violence last weekend, some of the worst unrest France has suffered in years, followed weeks of largely peaceful student protests and wider demonstrations over the cost of living and declining public services. French authorities imposed curfews in parts of several cities on Monday.
Reuters has contacted PSG, Lyon, the LFP and the Paris police prefecture for comment.