The 67-year-old Frenchman, whose contract expires this summer, said he will discuss his next steps with the board after the Gunners' FA Cup final against Chelsea next Saturday.
Arsenal trail fourth-placed Liverpool by a point with one game left in the season and risk missing a Champions League spot for the first time during manager Arsene Wenger's 20-year reign at the club.
Asked directly whether Sunday's match - on which their Champions League qualification hopes hinge - would be his last at the club's Emirates Stadium, Wenger replied: "I can not tell you that".
Arsenal are only in with a shout of the top four thanks to Sanchez, who played through the pain of a thigh injury to see off Sunderland, emphasising how much they need him to sign a new contract.
"I am capable to focus on what I think is important in life", Wenger said.
'Back in the day I said in an interview coaching wasn't Arsene's strong point, ' he wrote.
Striker Sanchez has admitted he will decide on his future at the end of the season and it is believed he could go if the Gunners fail to secure their usual place in the Champions League.
The Gunners now sit fifth in the Premier League, one point behind Liverpool in fourth.
If Liverpool beat relegated Middlesbrough and City avoid defeat at Watford, then Arsenal are consigned to the Europa League, but Wenger hasn't given up yet.
If Arsene Wenger guides his side to another season of Champions league football he will have increased his chances of remaining in charge at Arsenal.
"I am here to serve the club and the best way to do that is by winning the next game".
"Patrick Vieira once suggested Arsene does not like big characters and personalities around, especially ones from Arsenal's history".
'That's what we've done in the last three games. And though I modified that in the final article it didn't go down well.
"We have to do our job, we are professionals".
Well, Wenger did hit back in his Friday press conference, much to the amusement of fans and the media alike...
Arsenal are once again sweating on the fitness of Laurent Koscielny ahead of their final Premier League game of the season.
"I think no one has scored more goals in the Premier League as he did at his age".