Savic has struggled to gain regular starting appearances since his summer move to City, leading to speculation that he was keen on a switch to AS Roma.
However, representative Vlado Borozan has claimed that the Montenegro international is happy at the Etihad Stadium.
"Roma's interest in Savic? He will definitely be staying in Manchester," Borozan told notiziariosportivo.com.
"He is happy at City. Yesterday he played against United in the FA Cup.
"He absolutely will not be moving."
The 21-year-old is six months into a four-year contract with City.