It was reported that Arsenal agreed a fee with Manchester City for Sanchez to leave, but that the deal collapsed because the Gunners were unable to complete the signing of Monaco winger Thomas Lemar in time.
Sanchez cut a forlorn figure in the 4-0 defeat to Liverpool prior to the international break, over which he endured more misery with Chile in the World Cup qualifiers.
But Wenger has no doubts about the character of his star player.
"I have no doubt about Alexis' mind and mentality, that people question," the Frenchman said.
"He needs to come back to full fitness, which he was not (at) against Liverpool
It was his first game, and he has suffered a negative experience with Chile.
"But he is strong mentally and hopefully he will be back very quickly to his best."
Wenger would not go into detail on how close Arsenal came to selling Sanchez on transfer deadline day.
"The transfer market is over, there was a lot going on on that front
It's very difficult for me to speak about that because the most important thing now is our next game," he said.
Asked whether any Sanchez sale hinged on bringing in Lemar, Wenger added: "That's what I read everywhere, yes
My view is that it is too difficult to speak about that because Lemar is now in Monaco and of course Sanchez is here.
"I believe you have to keep a certain confidentiality about transfer negotiations
Many things happen at the last second."
Wenger quickly moved on to giving his backing to closing the transfer window before the season starts
Premier League clubs are expected to discuss bringing the deadline forward at a meeting on Thursday.
"It is important that we change that and close all that stuff before the championship starts," he said.
"You can see in the games even in the players' minds they have no clarity - are they in, are they out? - and are they being tapped up by people in the game who want to get them out?
"It is not a way to work and it is uncomfortable
It is time to kick that out before the season starts."
Wenger said it was "not true" the Lemar deal failed because the player was not interested in joining Arsenal.
"He decided to stay in Monaco and you have to respect that," he said.
"The player has a three-year contract to go - so overall you have to respect that."
Wenger would not disclose whether Jack Wilshere - who had a season-long loan at Bournemouth last season - would be in the Gunners squad to face the Cherries at the Emirates Stadium on Saturday.
He insisted there were no fears over Spanish playmaker Santi Cazorla's fitness, when it was suggested to him he may never play at the top level again.
"Santi is having his first run today," Wenger said.
"The flexibility of his ankle is good, his mobility is good, and now it's time to get him back to full fitness without any setbacks.
"It's difficult to predict when he will be available again - not before Christmas
But I hope after Christmas he will be available."
Cazorla has not played for Arsenal since October last year, when he was injured in the Champions League win over Bulgarian side Ludogorets.
Source : PA