Manager Arsene Wenger has previously revealed that talks on a new contract will wait until the season finishes, and Sanchez - the matchwinner in the 2-0 midweek win over Sunderland - will leave the decision over whether he stays or goes to the club.
The Gunners had to win to keep their top four hopes alive and thanks to Sanchez's goals, they are now one point behind fourth-placed Liverpool going into the final day of the season.
For a Champions League play-off between Arsenal and Liverpool, the final day results needed are Arsenal 1 - Everton 1 & Liverpool 0 - Middlesbrough 2.
"We won more games than previous year and we have one point more already". But Sunderland were far more willing opponents than they had been against Swansea at the weekend.
Sunderland, losers in nine of their last 12 games and relegated last month, were hardly a step up in class.
If Arsenal do miss out on the Champions League, Wenger has already pin-pointed the cause - a series of damaging away defeats. They play the way they want to play, so if teams of Tony Pulis want to play that way, perfect. "We have a good chance".
Reflecting on the possibility of securing a top-four finish, Wenger added: "Let's get to 75 points and see what happens".
Swathes of empty red seats at a hushed Emirates Stadium illustrated the apathy of some Gunners fans, the subdued atmosphere compounded by Arsenal failing to make their early dominance count. "I've seen the cup and I want to win it, that is the only thing I can say".
Sanchez has scored 28 goals in 49 appearances this season despite not being an out-and-out striker, but media reports have suggested he is unhappy at the club.
Harry Redknapp has claimed that the sale of Alexis Sanchez to Chelsea would lead to uproar from Arsenal's fans.
They still have the FA Cup final to prepare for, but first, Everton on Sunday.
I suspect this is just a diversion tactic for Mr Wenger. At the Emirates, they've won nine of their last 11 with Man City the only visitors to score against them in the last five.
"This is a situation, maybe some players don't feel great but you need to be focused on our job and have the best results for Arsenal".
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