The Gunners were interested in signing Sterling as part of a potential deal that would have taken Alexis Sanchez in the opposite direction to City during the summer.
However, the deal collapsed on transfer deadline day, with Sterling going on to establish himself as a key player in Pep Guardiola's squad this season.
The 23-year-old is City's top scorer in all competitions this campaign with 13 goals to his name, one more than Sergio Aguero.
Speaking ahead of City's trip to Manchester United on 10 December, Sterling said he had no intention of leaving the club any time soon.
"I'm happy at Man City at the moment," he told Mail on Sunday. "But nobody knows what the future brings so one day, definitely, it would be nice to play abroad. It would be a great experience.
"Spain's attractive. Anywhere the weather is nice really! Can't be in London. I can't be near my friends. They got to stay down there."
Sterling credited increased competition for places at the Etihad Stadium as one of the factors behind his sparkling form this season.
City signed Bernardo Silva from Monaco for £43m ($58m) in the summer to provide competition to Sterling and Leroy Sane.
"Bernardo Silva came in and that competition, stuff like that spurs me into trying to do well, to get better," Sterling said.
City are eight points ahead of United heading into the first Manchester derby of the season at Old Trafford.
Guardiola's side have won all but one of their league games this season, but suffered their first defeat in 29 matches on 6 December as Shakhtar Donetsk beat them 2-1 in Ukraine in the Champions League.