Wenger said Sanchez would only be allowed to leave if they could get a new signing over the line - the club have been linked with young Bordeaux forward Malcom.
Arsenal face Bournemouth at the Vitality Stadium on Sunday afternoon, but Sanchez has not travelled with the squad despite no reported fitness issues.
The 29-year-old is free to negotiate a move to a club overseas, or wait until the summer where he can join any club of his choosing.
I think it is a good investment.
"He never speaks about targets during the season, but as a football club Sanchez is one of those players, they will say if they do become available, you have got to be looking at it". We don't believe in signing a player just to do something.
Foreign clubs are free to offer the talented winger a contract from now but English clubs must wait until later to sign him for free unless they bid for him in the current January transfer window.
Paper Round's view: Jose Mourinho has never been a fan of Arsene Wenger, and signing both players would be a huge blow to his opponent.
" It looks like Sanchez will not extend his contract.These guys want to win, and they want to make money as well". But fresh speculation on Friday claimed that the Premier League leaders are cooling their interest.
Armenia global Mkhitaryan has struggled to hold down a first-team place at Old Trafford this season and Sky Sport Italia reports that Arsenal are keen on the former Borussia Dortmund forward.
It seemed as though the talented forward was settling in well with the Parisians, but Manchester United have registered their grave interest in the former Barca man, according to latest sources.
That could be less certain now though, Sanchez's preference is still understood to be City but if United go all out to sign the player he could easily change his mind.
While it wouldn't be a direct replacement for the Chilean from Arsenal's perspective, it does help fill the void while also potentially guarding against the likely departure of Mesut Ozil whose contract runs out in the summer as well.