The 67-year-old has been in charge of the Gunners for more than 20 years but has seen his position come under increased scrutiny following the 5-1 thrashing at the hands of Bayern Munich on Wednesday night.
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Arsenal boss Arsene Wenger is expected to step down as manager when his contract runs out at the end of the season.
Sanchez's Gunners future has been a matter of intense debate in recent months, with the Chilean said to be unhappy with the club's failure to challenge for major honours during his time at the Emirates Stadium.
And, speaking after the heavy defeat, a dejected Wenger said: "It was a odd game because I feel in the first half we played quite well and we had two good chances just before half-time".
"We play at home so we want to put pressure on them from the very first minute". He says he will still be managing next season so I am assuming that to mean he will still be at Arsenal. Arsenal legend Martin Keown called it probably the lowest point in Arsene Wenger's 20-year stint and suggested Wenger must think about hanging up the boots. "I am in a public job, I accept that and I have to behave with my values and accept everyone can have an opinion".
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However, Wenger is maintaining his focus as Arsenal resume their FA Cup campaign at non league Sutton United this weekend.
"I feel for Wenger now.it's embarrassing".
"A defeat like that, it was hard to take but we have the strength and the experience to respond to it". We have to focus on real problems, the way we play football and not my future.
Bayern Munich answered its critics with a comprehensive 5-1 rout of Arsenal in the first leg of their Champions League clash to move a step closer to the quarterfinals on Wednesday.
In 2013 Giroud and Laurent Koscielny scored the goals in a 2-0 win, and Kolo Toure netted in 2005 as Arsenal went down 3-1.
He explained that to win the Champions League "you have to have courage, personality, experience and luck", - but - he underlined the word again while purposely omitting others for emphasis: "You need courage". "We looked vulnerable from that moment onwards and the last 25 minutes were a nightmare for us because we had no response". "You have to accept that".