The Daily Star have reported today that the towering Bosnian striker is on Wenger's radar as he seeks a new forward to provide competition with Olivier Giroud.
The 29-year-old Dzeko is also reportedly coveted by Italian side Roma.
With Raheem Sterling having already arrived at the Etihad Stadium, Dzeko has fallen even further down the pecking order at City.
Dzeko made 22 appearances in the Premier League for City last term, but only started 11 of those matches.
Arsenal were in pre-season action yesterday, beating Everton 3-1 in the Barclays Asia Trophy final in Singapore.
Wenger handed a debut to new signing Petr Cech and saw goals from Theo Walcott, Santi Cazorla and Mesut Ozil secure his side victory in front of a crowd of 53,000 at the National Stadium.
Arsenal had sealed their place in the final by beating a Singapore Select XI 4-0, while Everton won through against Stoke after a penalty shootout.Reuse content