The 21-year-old has turned in a number of impressive performances for the north London club this season, with his fine form recently earning the defender his first England international call-up.
Citizens boss Roberto Mancini was keen on signing Jenkinson before he joined the Gunners in a £1million deal from Charlton Athletic in 2011, and is ready to reignite interest in the summer.
Arsene Wenger will be determined to keep hold of the talented right-back, though, with Bacary Sagna likely to leave the Emirates Stadium at the end of the campaign.
Arsenal turned down offers from Stoke City and Wigan Athletic to take Jenkinson on loan in January, with Wenger believing the player's development would be better served in north London.
After signing a new long-term deal at the back end of last year, Manchester City don't hold much hope of signing the former Finland U21 star, who is a life-long Arsenal supporter.
The reigning Premier League champions are committed to buying the best up-and-coming talent, however, and so will consider an approach if Jenkinson does become available.
If the unlikely transfer does happen, it wouldn't be the first time that an Arsenal player would make the move north, following the likes of Emmanuel Adebayor, Kolo Toure, Gael Clichy and Samir Nasri to the Etihad.