The Shakhtar Donetsk star impressed in two Champions League ties against City this term and boss Pep Guardiola is believed to have instructed director of football Txiki Begiristain to try and make a deal happen.
A transfer this month is highly unlikely but the Citizens are not put off by his £30million price tag and Fred is seen as an ideal back-up and long term successor to his compatriot, Fernandinho, who took exactly the same route from Ukraine back in 2013.
It's understood Fred is aware of the moves behind the scenes and would jump at the chance of joining up with City's growing stable of Brazilians, which also include Gabriel Jesus, Ederson and Danilo.
Guardiola knows Manchester United and Chelsea have both been linked to Fred and that is why he has tasked City to try and see if they can put something in place as quickly as possible.
Fred is more of an attacking midfielder but Pep feels the South American has the technical capacity to adapt and can develop the defensive side of his game under his coaching.