The Gunners trail City by 12 points, having already suffered four defeats in their opening 12 fixtures, but the mood around the club has lifted after a comfortable 2-0 win over north London rivals Tottenham over the weekend.
City have been in imperious form of late and have dropped just two points in the league all season, but Xhaka feels Pep Guardiola's side will suffer a drop in form at some point during a long season.
"I think in football everything is possible," the Switzerland international told Sky Sports.
"Manchester City, at the moment, are on a very good run, they're doing very well and others have dropped points – which they haven't done – but it's conceivable that they could drop points as well. They might not continue as they have been.
"But our aim is just to focus on ourselves. We know we need to work and we're convinced that we can compete at the top.
"Everything's possible, I'm a person who thinks realistically but has dreams and fantasies as well. In football, everything is always possible," Xhaka added.
Manager Arsene Wenger admitted after the win over Tottenham that it would be tough for Arsenal to chase down Manchester City, whose recent performances he described as "from another planet".
The Frenchman revealed that he was still miffed with the controversial refereeing decisions that marred the Gunners' 3-1 defeat to City at the Etihad Stadium earlier this month.
"Manchester City is on another planet with the results," Wenger was quoted as saying by the Daily Mirror. "That's why, two weeks ago, I was so angry because they didn't need that help."
Arsenal travel to Cologne in the Europa League in midweek before a trip to Turf Moor to take on Burnley on 26 November.