According to the Guardian, the Ligue 1 side want both players and have the financial might to pull off the deals, in what would be an enormous coup for the club.
The report claims the club’s sporting director Antero Henrique met Sanchez and his agent on Friday in Paris and are close to agreeing a deal with the player.
They are also hopeful that the potential arrival of Neymar from Barcelona, will help persuade Alexis his future lies in France.
The club are subsequently expected to make an opening offer of €45 million (£40.3m) to Arsenal for the Chilean, and the club are confident they can strike a deal, with chairman Nasser al Khelaifi enjoying a good relationship with Arsene Wenger.
The Guardian goes on to state that PSG expect their initial bid to be rejected and, if so, will follow it up with an improved €50m (£44.8m) offer.
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Wenger continues to insist Arsenal will not sell Sanchez, but it looks as though his resolve is set to be truly tested with an offer from PSG.
Although the Gunners clearly do not want to sell Alexis, he has made it fairly clear he will not sign an extension currently, and a large offer from a foreign club may prove tempting.