The 28-year-old, who is one of Arsene Wenger's most important players, currently earns £130,000-a-week at Emirates Stadium.
But discussions over an extension has failed to progress in recent months with Sanchez's representatives keen to agree a deal which would see the Chile international's salary double to bring him in line with other top Premier League earners.
Standard Sport understands Arsenal will demand a transfer fee of close to £50million for Sanchez if a new contract is not signed and the player has suggested he would be happy to allow his contract to run down.
"I am happy in London and I hope to finish my contract at Arsenal," Sanchez, at a press event in Santiago, is quoted as saying by Chilean newspaper Publimetro.
"I like to stay in a city and in a team, but in a team that is a winner, that has a winning mentality."
Sanchez has scored 22 goals in 38 appearances for Arsenal this season and losing his services would represent a severe blow at a critical time for the club.
Mesut Ozil is also about to enter the final year of his deal while Wenger is yet to confirm whether he will extend his spell in charge, with his own contract set to expire this summer.
The Gunners have failed to win any of their last five top-flight games and are in danger of missing out Champions League football next season, which would also be expected to have a bearing on Sanchez's future.
The forward played 90 minutes in both of Chile's fixtures during the international break and is set to be assessed by Arsenal's medical team ahead of Saturday's clash with Manchester City, having picked up an ankle problem in a 3-1 defeat to West Brom on 18 March.