Sanchez was understood to be on the verge of joining the Premier League leaders and his former Barcelona boss Pep Guardiola in August, only for Arsenal to pull the plug on the move when they were unable to secure a replacement.
Fresh reports emerged this weekend regarding the 29-year-old retaining a desire to move to the Etihad Stadium, perhaps as early as January, with his Arsenal contract up at the end of this season.
The Guardian claimed Sanchez was at the centre of a dressing-room bust-up following last month's 1-0 win at Burnley, while Arsenal great Thierry Henry believes the split celebration to one of the star's two goals at Crystal Palace last time out demonstrated a schism within the squad.
Wenger will chalk up a landmark 811th Premier League game in charge of Arsenal when they travel to basement boys West Brom on Sunday, surpassing Alex Ferguson's number of games managed in the competition, and relentless talk regarding Sanchez's commitment to the Gunners' cause soured the Frenchman's mood ahead of what should be a celebratory occasion.
"When he plays well it's a problem," he told reporters. "When is it not a problem? It's unbelievable.
"You judge a player on whether he played well or not and you comment on it after that.
"I am not a psychologist to know what is in his head, if he is short-term or long-term.
"You turn up to play football, that’s it. After that you judge, did he play well or not well."
13 - Alexis Sanchez has had a hand in 13 goals in his last 15 Premier League London derbies (10 goals, 3 assists). Capitalised. pic.twitter.com/nwpXvGZSAd— OptaJoe (@OptaJoe) December 28, 2017
Wenger was more willing to discuss another of his players who will be out of contract in June.
Jack Wilshere has put an injury nightmare and an unproductive loan spell at Bournemouth behind him to reassert himself in the Arsenal first-team picture this term and his manger hailed the 25-year-old's mental strength.
"It is better when we talk about that," he said. "Give him credit for what he has gone through. His performance [against Palace] deserves credit because it demands some character.
"I have a big respect for that because it is all nicey-nicey when you are super-talented and everybody says you are the greatest player at 17, but to come back to that level when you have gone through what he has gone through shows a special character.
"I never feared for his career because in my job a very important quality is always to continue to believe in human beings. I believe everybody is alive to fight."