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.”