The 21-year-old is the Bundesliga's top scorer this season and has also attracted interest from Barcelona and Chelsea, with the Catalans understood to be at the front of the queue for his signature.
The striker is on a two-year loan from Benfica and Frankfurt are hopeful they can trigger a clause to sign him outright for €6 million (£5.3m/$6.8m) this summer, before selling him on for €60m (£52m/$68m).
Barcelona, for their part, hope to sign him for €40m (£34.3m) and that kind of price would appeal to City, who have prioritised other areas for reinforcement in the upcoming transfer window.
The Premier League champions will move for a holding midfielder and a left-back, but sources have told Goal that they have been monitoring Jovic closely in recent months.
It is not yet clear whether City are ready to make a concrete move, as the Premier League club have form when it comes to biding their time over transfer targets.
This time last year, for example, they were tracking Tanguy Ndombele before he made his loan move from Amiens to Lyon permanent. City prioritised a move for Jorginho instead but have now returned to Ndombele, who features heavily in their summer transfer plans.
Likewise, they held several meetings with Ajax centre-back Matthijs de Ligt's representatives at the end of last season, but never held any hope of actually signing him in the summer of 2018. The Dutchman remains one of the club's targets, however.
Jovic has scored 15 Bundesliga goals this season, two more than Bayern Munich's Robert Lewandowski, who is second in the Bundesliga golden boot standings.
The Serbia international became Red Star Belgrade's youngest goalscorer when he opened his account at just 16 years of age, and this season he became the youngest player in Bundesliga history to score five goals in a single game.
City are always on the look-out for new players from across the globe and it is no surprise Jovic is on their radar, although it is understood that the club's interest in him goes beyond merely including him on a long list of talents.
It is possible that City would move to secure their priority summer transfer targets first - Leicester's Ben Chilwell is an option for left-back - before assessing their situation regarding Jovic.
City regularly attempt to tie up their 'A list' signings as early as possible before assessing the state of the market later in the summer.
In 2018, for example, they monitored the situations of Eden Hazard and Kylian Mbappe, separately from their attempts to bring in top targets Jorginho and Riyad Mahrez.
Goal understands that, while Barcelona are keen on Jovic, they are also looking at Andre Silva and Maxi Gomez, and the Catalans' movements in the market could also influence City's plans.