The Chile international has been linked with the Emirates Stadium exit all summer after letting his contract run into its final year.
Manchester City, Bayern Munich and Paris Saint-Germain have all been credited with an interest in Sanchez, who returned to training this week following an extended summer break.
According to The Sun , however, PSG are unlikely to further their interest as they are on the brink of landing Neymar from Barcelona for £196m, while Wenger has also ruled out selling his prized asset to a domestic rival.
Wenger is said to have offered the 28-year-old another chance to put pen to paper on the mega-money deal offered to him earlier this year, worth in excess of £290,000 a week, which will likely put an end to the speculation over his future for at least the next 12 months.
Sanchez contributed to 34 goals in 38 Premier League games last season, while also playing a part in a further nine in cup competitions.