The Socceroos winger is expected to join Celtic on a long-term loan deal, according to Sky Sports.
The 19-year-old featured in each Australia's group matches at the World Cup.
Arzani, who was born in Iran, made his debut for City in January this year and eventually won the A-League Young Footballer of the Year award.
We are delighted to announce the signing of Daniel Arzani from @MelbourneCity! #mancitypic.twitter.com/55SoNc8qRK
— Manchester City (@ManCity) August 9, 2018