Fernandinho has been photographed leaving a hospital in Manchester where the club conduct their medicals and City are set to secure a deal for the Brazilian.
Manuel Pellegrini is expected to be named as City's new manager in the next few days and the club have already started to strengthen their squad after relinquishing the Premier League title.
City agreed a deal for Sevilla winger Jesus Navas earlier this week and they now appear to have landed long-term target Fernandinho.
The 28-year-old made a big impact on these shores last season when he scored Shakhtar's winner against Chelsea at Stamford Bridge in the Champions League group stages.
He has been repeatedly linked with a move to England as both Chelsea and Tottenham failed with bids in the last 12 months.
Reports suggested the Ukrainian club had inserted a buy-out clause of £42.5million for Fernandinho, who complained about his high valuation.
He has admitted his interest in joining City as he feels the switch will stengthen his chances of being selected for Brazil's World Cup squad.
"They know that the Premier League is a great championship and that Manchester City is a great club, therefore they all wish me to play there, and to participate in the division," he has said.
"I believe my chances of making the World Cup squad will improve if I join City.
"My exposure would be better, because Brazil is biased towards the Ukrainian league. What we do here is not recognised in my country."