The Ligue 1 giants have been among the many clubs strongly linked with the Chile international in recent times, as he stalls on signing a new contract at the Emirates Stadium.
Sanchez has been in terrific form for the Gunners this season, but his deal is set to expire at the end of next term, which could lead to a departure on the cheap this summer.
Arsenal have reportedly been eager to avoid selling Sanchez to rivals Chelsea or Manchester City, with claims that they have actively invited interest from PSG in his signature.
Reports from Yahoo France now claim PSG will try their luck with an opening bid of around £46million to bring Sanchez to the Parc des Princes in the summer.
In a potential double blow for Arsenal, the report also claims PSG are sniffing around for Mesut Ozil, who is in a similar contract situation to that of Sanchez.
Arsenal recently put off further contract talks with their star duo until the summer, but it looks increasingly like they will struggle to keep two of their most important players in north London.
Sanchez recently expressed a desire to remain in the UK capital, hinting at a potential move to Chelsea, but PSG seem to be leading the chase in terms of concrete interest at the moment.