According to The Independent's Jack Austin, the Gunners are "desperate" for Sanchez not to join a fellow Premier League side if he does move on this summer, but their £50 million valuation and the Chilean's £300,000-per-week wage demands proved prohibitive to Bayern Munich.
Inter could be set to enter the fray, though, as La Gazzetta dello Sport (h/t Austin) said the Serie A club want to make him their "poster boy," and with the financial might of their Chinese owners, they can afford his wages.
The club are hoping to keep pace with bitter rivals AC Milan, who have splashed the cash this summer in their bid to resume their status as a giant in Italian football once again.
Arsenal would naturally prefer the 28-year-old to stay put after he bagged 30 goals in all competitions last season, but he's yet to sign a new deal at the club with just one year remaining on his contract.
His wage demands could well be a sticking point, with the Mirror's John Cross reporting Sanchez is using interest from China to justify them:
City would likely have little trouble offering the former Barcelona man a satisfactory sum, but Arsenal can ill afford to let him join the Sky Blues.
Doing so would be tantamount to guaranteeing their inability to finish above City in the Premier League next year, such would be the strength of their firepower if he joined the likes of Sergio Aguero, Gabriel Jesus and Bernardo Silva.
James Robson of the Manchester Evening News gave his take on Arsenal's situation:
Aside from Sanchez staying, his departure abroad is the ideal scenario for the Gunners this summer, and he would mark a real statement of intent from Inter, too.
However, the Nerazzurri have fallen away from Europe's elite in recent years, so at this moment in time they would represent a step down from Arsenal given they don't even have UEFA Europa League football to offer, let alone the UEFA Champions League.
As such, even if they are willing to spend the money needed to get Sanchez, he may not be open to joining.