Sanchez, 28, was expected to make the move to City during the transfer window, but no deal was agreed despite a £60 million bid being tabled.
Wenger believes the Chile international, whose contract expires in 2018, will perform for Arsenal as the Frenchman revealed a deal was never close.
"Your interest is always to perform," he told beIN Sports.
"It was not very close and it's very difficult for me to speak about that because what I want from the player now is to focus on his career, on his season and on Arsenal Football Club."
It was believed Arsenal were willing to let Sanchez leave, if they landed Monaco's Thomas Lemar.
Wenger hinted that was the case after revealing the 21-year-old rejected a £90m deadline day switch.
"I cannot tell you everything that happened because after that when you decide to let a player of that calibre go, you need to replace him because nobody would understand that you let the player go," he said.
"When you cannot do it, you keep the player and you make a financial sacrifice because at the end of the day what you want is to have a team that has good potential and top quality.
"That means Alexis Sanchez will go in like Mesut Ozil, it's similar, you go into the final year of his contract, or you think that during the season you find a way to extend the contract, or at the end of the season the players go for free."
Arsenal have made a slow start to the Premier League season, losing two of their opening three games to sit 16th in the table.