The former Germany global, speaking after Arsenal's 5-2 Emirates Cup win over Benfica, said he was excited about "getting an opportunity to work here and inspire young people".
Sanchez was due back at Arsenal on Sunday, but his return to England has been delayed by at least 48 hours after he caught the flu, revealing the illness with a social media picture of himself huddled under a blanket with the caption "sick".
"There's no development - he is staying, of course".
However, that could all change on Tuesday when Sanchez finally returns - just five days before Arsenal face Chelsea in the Community Shield - with The Mirror reporting that he is considering handing in a transfer request to try and force through a move to Manchester City.
A host of top clubs are believed to be interested in signing the former Barcelona forward including PSG, who Sky sources understand are willing to offer him £250,000 per week.
Claudio Bravo has told Alexis Sanchez that he will be welcomed with open arms if he swaps Arsenal for Manchester City this summer. Nobody knows if Sanchez will not extend his contract here.
As many as eight Arsenal first-team players now have one year remaining on their deals at the Emirates Stadium, most notably the likes of Alexis Sanchez, Mesut Ozil, Alex Oxlade-Chamberlain, Jack Wilshere and Santi Cazorla.
Arsene Wenger however, insists that there is no need for alarm. "I competed for my team-mates, who wanted me to play, and because I wanted to reverse the situation of not having had a good year".
"Do you really think that you sit in the dressing room before the game and think, "Oh I only have one year to go I will not play well today"?"
"He has flu. I had him on once the player is done or not done".
Sanchez's future remains up in the air as he enters the final season of his current contract, with talks over a new deal seemingly at an impasse.