City could strike a double early blow in the transfer market as they close in on the signing of Jesus Navas as well.
Fernandinho was reportedly spotted in Manchester for a medical ahead of a rumoured £34million move to the Etihad Stadium.
Signing the Brazilian would come soon after a deal for Sevilla winger Navas, which was confirmed, subject to a medical, by the Spanish club earlier in the week.
City, who are also believed to be close to appointing Manuel Pellegrini as manager, have not commented on either prospective transfer but there are not understood to be any problems.
Both seem likely to be confirmed in the coming days along with the arrival of Pellegrini, who has been tying up loose ends after announcing his departure from Malaga.
It appears City intend to act decisively as chief executive Ferran Soriano and director of football Txiki Begiristain get their first full summer transfer window in which to operate in tandem since joining the club.
City's failure to land any of their prime transfer targets last summer was regularly cited by former manager Roberto Mancini as one of the reasons for their regression last season.
The new manager may not yet be in place but City have made clear it will be Begiristain who drives their player recruitment policy.
City are thought to have been tracking Fernandinho, who shone against Chelsea in the Champions League last season, for some time and the 28-year-old has spoken of his desire to join the club.
His Shakhtar contract reportedly contained a £42.5million release clause but City may have been able to negotiate a compromise.
Spain World Cup-winner Navas is thought likely to cost City an initial £17million.
The 27-year-old has expressed excitement at his impending move, saying he is joining a "great club".
City have also been strongly linked with Malaga playmaker Isco and he could follow Pellegrini to the Etihad Stadium.