Arsenal go into this weekend's Saturday Night Football game now 100/1 outsiders for the title in the wake of a 6-0 hammering at Chelsea and Tuesday's failure to beat Swansea.
The first of those results led to fresh speculation Wenger could walk way when his deal is up this summer, while a 2-2 draw in midweek means fifth-placed Everton are now just six points behind with a game in hand and a home fixture against Arsenal to come next week.
But on the eve of City's visit Wenger made it clear his long-term plans have not changed and said he is entirely focused on bridging another six-point gap - to leaders Chelsea - in the remaining seven games.
"There is no other priority other than coming first," said Wenger. "That is still our target.
"Champions keep going when everybody else would give up. We have an opportunity to show that we have that mentality.
"If people say Everton can catch us then we can catch the teams above us. We have not given up, believe me. It's our attitude tomorrow which will show that.
"It is the next game that is of course very important, and the next game is of massive importance because it is Man City and they fight at the top.
"They are the favourites with Chelsea and Liverpool, but when you play one of the favourites, you have an opportunity to shorten the distance to them."
Arsenal were beaten 6-3 at the Etihad in December but have not lost a league game at home since the opening day of the season, and Wenger said: "We play at the Emirates where we show big strengths and we want to show that again.
"There are plenty of positives to take from the game at the Etihad. But of course we must defend better."
Wenger was asked about criticism from former Manchester United player Paul Scholes, who this week said Arsenal are "a million miles away" from winning the title.
He said: "If six points is a million miles away...I don't know what the translation of a mile into a point is. People who have managed zero games have opinions and we have to accept that."
Wenger has now managed more than 1,000 games at Arsenal, but he is yet to commit publicly to extending his contract beyond the end of the season.
Recent setbacks, and his decision to cancel a press conference ahead of the Swansea game, led to speculation he could yet decide to leave this summer.
But senior figures at the club have consistently said the manager will sign a new deal, and Wenger said: "My commitment is not questionable. I have given my word, and I always respect my word."
Bacary Sagna's contract is also up this summer, and Inter Milan's president this week claimed the right-back has decided to stay in England.
That prompted reports linking Sagna with Manchester City, but Wenger said: "I'm confident he will stay, but we will accept his decision and go with it."
Watch Arsenal v Manchester City live on Sky Sports 1 this Saturday. Coverage begins at 5pm