The 23-year-old is due to make his Arsenal debut after joining the club from Manchester United for a reported £16m fee on transfer deadline day last Monday.
The North London outfit are unable to call on striker Olivier Giroud as the Frenchman continues to nurse a broken foot.
In this morning's press conference, Wenger said: "I cannot tell you if Welbeck will start [against City] but it's a possibility. I have to assess the squad. Danny Welbeck is young and I feel he can improve his career here - he is confident."
Welbeck scored both goals in England's 2-0 victory over Switzerland in Euro 2016 qualifying on Monday.