The Montenegro international only joined the Sky Blues last year in a big money switch from Fiorentina, where he had developed a reputation as one of Europe’s top emerging talents.
However injury problems have plagued Jovetic’s debut season in England, leading to speculation that he could be sold in the coming months.
The player himself has indicated that he is ready to stay and prove himself, but there have been whispers that City are prepared to cut their losses on the versatile forward.
This has alerted Roma, who are keen to offer him a route back to Italy.
The 24-year-old was impressive in Serie A prior to his move to the Premier League, and despite his troubles his reputation with the division’s big teams has not faltered.
The Rome giants are believed to be ready to spend big this summer as they plan for a likely return to the Champions League, and are understood to see Jovetic as an ideal marquee attacking signing.