The deal is worth 55.4 million pounds according to a BBC report, with the Belgian international set to travel to Manchester on Tuesday to complete a medical.
He has 16 caps for Belgium and made his debut in 2020. He was called up to the squad for the World Cup in Qatar last year, making one appearance off the bench before Belgium were eliminated in the group stage.
Pep Guardiola's City are looking to boost their attacking options after the departure of Algerian forward Riyad Mahrez (32), with Doku's signing bolstering the league champions' ranks as they chase a fourth successive title.
City are second in the Premier League standings with six points from two games. They travel to face newly-promoted Sheffield United on Sunday.