The Chilean was linked with a move to Arsenal's Premier League rivals Manchester City throughout the summer transfer window.
But after staying at the Emirates beyond the deadline, PSG are now ready to use their embarrassment of riches to lure Sanchez to the French capital.
The Ligue 1 outfit signed Neymar from Barcelona for a world-record fee of £198m over the summer and also secured the loan move of young prodigy Kylian Mbappe.
But it seems they are determined to beat Pep Guardiola's side to another huge signing.
According to El Mercurio, PSG are prepared to give Sanchez a £9m signing-on fee in the New Year, if he decides to join the club.
The Arsenal forward's representatives met with PSG chiefs over the summer but the club baulked at his £400,000-a-week demands.
But with Edinson Cavani looking likely to leave after a bust-up with Neymar, PSG may be able to offer Sanchez the bumper deal.
The 28-year-old's Arsenal contract runs out in 2018 and the player has expressed his desire to leave the club.
The Gunners may decide to cash in on the player in January, rather than letting him leave on a free next season.
Sanchez was close to joining Manchester City on deadline day.
However, the move fell through after Arsene Wenger failed to land Monaco winger Thomas Lemar as his replacement.
