According to Sky Sports, the two clubs have reached an understanding for a double swoop which also includes Emerson Palmieri.
The 23-year-old left-back’s entourage is expected to fly to London to wrap up the deal.
However, Dzeko’s personal demands have held up proceedings. The Bosnian is seeking a two-year contract at the very least but Chelsea’s policy for players over 30 is to only offer one-year contracts.
Chelsea have reportedly been in the market for strikers this month having been linked to the likes of Andy Carroll and Ashley Barnes.