The former Manchester City striker started his professional career with Zeljeznicar and after a few spells elsewhere, he moved to Germany to link-up with Wolfsburg.
It was there that Dzeko discovered his best form which then earned him a switch to Manchester City, but he was largely a bit-part player at the Etihad.
The Bosnia and Herzegovina striker has since moved on to Roma, where he is in scintillating form this season – scoring ten goals in 12 Serie A matches this season.
And it appears Dzeko took a tip or two off the goalscoring prowess of former AC Milan and Chelsea hitman Shevchenko.
“When I was growing up it was Andriy Shevchenko,” Dzeko told Roma’s official website. “I used to watch a lot of Serie A games because it was the best league at that time, and for me he was the best striker around. I remember his games for AC Milan, of course, but I also remember him for Dynamo Kiev – I remember the hat-trick he scored against Barcelona at the Nou Camp.
“That was probably the first time I saw him; I can’t remember exactly because it was a long time ago. But for me he was the No. 1 player.”
Dzeko also revealed how the toughest opponent he has come up against is Real Madrid’s Sergio Ramos, whilst also reserving praise for the fantastic Santiago Bernabeu.
“It is difficult to say,” Dzeko said, when asked who the toughest player he has faced was. “I have played against so many good defenders, sometimes it was much harder to play against smaller teams, against defenders who are not so popular like the other defenders. So I don’t know about the strongest.
“If I had to think about one I would perhaps say Sergio Ramos – I have played against him so many times for Manchester City, Roma and the national team. He is definitely up there with the best defenders I have faced.
“The Santiago Bernabeu is one of the most beautiful. There are so many others, like the Nou Camp, but there is something special about the Bernabeu. It has the history to it, and also the way to is designed – with the stands rising so high, so vertical – is impressive.”
And as for the best teammate Dzeko has had, the 30-year-old chose the silky David Silva, who played alongside the Roma forward at Manchester City for four years.
“Another difficult one! I have played with so many good players but probably the best I’ve played with is David Silva. I used to call him ‘little magician’ because this guy was brilliant with his feet, he could take any ball you gave him, control it, and pass it on.
“All of us were always amazed by his ability and technique. He is definitely the best I’ve played with.”