Reports claim the 19-year-old is set to join the Viola in a £12million deal.
Nastasic has long been linked with a move to Eastlands.
City defender Stefan Savic is expected to join Fiorentina as part of the deal.
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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.