The Chile international has been at the centre of speculation for months now after failing to agree a new contract at the Emirates.
Paris Saint-Germain and Bayern Munich were said to be early contenders for his signature, while Chelsea and Manchester City have also reportedly expressed an interest.
It has been widely reported that Sanchez is angling for a switch to Pep Guardiola's City, but according to The Times, Arsenal have ruled out selling him to a direct rival.
It is believed that the Gunners, who signed the attacker from Barcelona in 2014, would be more open to cutting a deal with a club abroad, but only if the price is right.
The North London outfit have offered Sanchez a new deal worth £275,000 a week, but the 28-year-old is after a bigger salary.