The Montenegrin attacker only joined the Sky Blues from Fiorentina over the summer, but has struggled to establish himself under Manuel Pellegrini.
After initial injury worries, Jovetic has found himself slip down the pecking order with fellow arrivals Alvaro Negredo and Jesus Navas impressing in his two preferred roles.
The 24-year-old’s struggles have alerted a number of Serie A sides, who are keen to offer him a switch back to Italy for regular playing time.
However, City are far from keen to let him leave, and will battle any potential January offers, despite the player himself failing to adapt to life in Manchester.
Jovetic’s agent recently said that his client is perfectly happy at the Etihad Stadium, but privately the versatile attacker is believed to be struggling to adjust to his new surroundings.
Pellegrini feels that once the player is fully fit and can feature regularly for his side that these problems will evaporate, and is keen to keep him at the club for the latter stages of the season to ease the process.