The Russian was in impressive form for his nation during Euro 2012, and is eager to make the move to Serie A in the future.
"Roma have a great young team with a great future and I think it'd be a great opportunity for me," he told the Corriere dello Sport. "Just thinking about it seems like a dream. Everyone knows who Zeman is. They know he likes football, and his style would suit me as I'm an attacker.
"I like Italian football, I think I would fit in very well. I can play on both wings, I think I know how to combine technique and vision."
Russia is currently home to two Italian coaches, Luciano Spalletti of Zenit and Fabio Capello of the national team, and Dzagoev went on to voice his respect for both.
"Spalletti is a great coach. He has brought his wealth of experience and adapted well to our football," he said. "I've been working with [Capello] for four months. It soon became clear that he's a coach of the highest level."