ESPN reported in February that the Croatia midfielder was one of several players likely to be made available as Chelsea plan a host of summer exits to trim their bloated squad and new manager Mauricio Pochettino will not stand in the way of his departure.
The 29-year-old has one year remaining on his contract and there have not been any meaningful conversations over an extension.
Although no fee has yet been agreed, sources suggest Kovacic has been given permission to discuss terms with City. Chelsea are thought to be willing to let him go for a fee in the region of £35 million.
City boss Pep Guardiola is keen to bolster his midfield options ahead of next season.
It remains to be seen if Ilkay Gundogan commits himself to City with his contract due to expire at the end of June -- Barcelona and Arsenal are among the interested clubs should he decide to leave -- but Kovacic would be a useful replacement given his experience with Chelsea, Real Madrid and Inter Milan.
Kovacic joined Chelsea from Madrid in 2018 -- initially on loan before the move was made permanent a year later for £40m -- and has made 221 appearances in total, winning the Champions League, Europa League, Club World Cup and UEFA Super Cup.