Sanchez is entering the final year of his Gunners deal and will be free to sign a pre-contract with another club in January.
Real Madrid, Chelsea, Manchester United and Manchester City, who were on the verge of signing the Chilean on deadline day, are all believed to be pursuing Arsenal's star man, but reports now suggest PSG have gained the upper hand in the race to land his signature.
According to the 'Daily Express', The French giants are prepared to offer Sanchez a mega £10m 'welcome' bonus to convince him to sign with them in January.
Like Manchester City, PSG were also interested in acquiring the former Barcelona man's services this summer and offered a £275,000-a-week deal, but Arsenal were determined to keep hold of their talisman, even if he decides to leave on a free in 2018.
Arsene Wenger was not prepared to risk a supporter backlash by selling Sanchez to Premier League rivals City, but it is understood Pep Guardiola is not ready to give up in his attempts and hopes he can finalise a cut-price deal for the 28-year-old when the transfer window reopens.