The 27-year-old is thought to have caught the eye of City manager Roberto Mancini with his performances for Shakhtar in the Champions League this season. In particular, the Brazilian received high praise from numerous pundits for his displays against Chelsea.
While the club's interest is only at an early stage, City believe that they will have to offer at least £17m to convince their Ukrainian counterparts to part with their player, according to The Guardian.
The report went on to claim that Fernandinho would replace Gareth Barry, who has been tipped to depart the Etihad Stadium over the coming months.
Fernandinho's contract with Shakhtar does not expire until 2016.