Juve failed with attempts to sign Robin van Persie and Fernando Llorente this summer.
Now their attentions have turned to Dzeko, with representatives watching him as Manchester City played Borussia Dortmund this week.
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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.