According to the Sunday Express (via Metro), Les Parisiens could offer the Chilean a £10 million bonus to sign the deal. El Mercurio previously reported on a £9 million bonus (h/t Tom Sheen of The Sun).
Per Metro, Sanchez nearly joined Manchester City during the summer transfer window and the Cityzens remain among the favourites to land him next summer. The former Barcelona man will be a free agent, and he's not expected to sign a new deal with Arsenal.
The 28-year-old is free to sign a pre-contract with a non-Premier League side in January, which would allow him to move to his new club at the end of the season. With no transfer fee involved, suitors are likely to offer big bonuses and a signing-on fee instead.
Arsenal could opt to sell the player in January but are unlikely to do so―the Gunners are instead expected to keep hold of Sanchez until the last minute, hoping the loss of transfer fee will be offset by a spot in next year's UEFA Champions League and the riches that come with it.
Sanchez has only started two Premier League matches this season, with injury limiting him early in the campaign. When he has played, he's been far from his best, feeding reports he has lost interest in the Gunners and that his mind is already elsewhere.
As SPORTbible noted, fans have not been impressed:
He remains one of the team's best players when in form, however, and he could have a major role to play in Arsenal's bid to finish the Premier League season in the top four.
Convincing Sanchez to sign a new deal seems next to impossible, and the key moving forward should be to ensure the January transfer window doesn't become a major distraction. Perhaps PSG offering a massive bonus is a good thing―it could ensure negotiations are quick and painless, and the player could swiftly shift his focus back to the pitch.
It could also make things interesting in the French capital. If Sanchez were to sign a pre-contract with PSG, it would put the spotlight on Edinson Cavani, who seems the likeliest to be moved to make room for the Chile international.