Van Dijk completed a £75 million transfer to Liverpool at the beginning of the window.
The Gunners want in excess of £30m for the Chilean worldwide, despite knowing he will be free to walk away for nothing in the summer.
The 29-year-old has less than six months remaining on his current deal to throw up the possibility of the South American leaving for nothing at the end of the season.
Sunday's 4-2 defeat at Nottingham Forest compounded Wenger's frustrations, with the Premier League already out of reach.
The Gunners will demand £40 million if City try and steal away their prized asset and while City believe Sanchez would join them in the summer and would prefer to pay less, they proved last August they aren't afraid to pay big to get their man early.
Now, with the January transfer window wide open, things might work out.More news: National Football League investigating Panthers again for potential violation of concussion protocol
At this point it is more a matter of when, not if, Alexis Sanchez will leave Premier League giants Arsenal.
- The Guardian say that City have not made a bid yet, but that one will be made worth £30m in the next few days.
Goal understands City are keen on the Shakhtar Donetsk midfielder as Guardiola looks to add depth to his squad in the middle of the park.
In fact, the future of Alexis Sanchez can certainly be deemed a saga of its own.
Sanchez is said to be "desperate" to seal the move to Pep Guardiola's team and considering how the two sides are performing right now, it's easy to see why.
City's interest in Sanchez has been longstanding, as they failed in a late bid in the summer to bring him to the Eithad Stadium, as noted by Lee.