The Viola are interested in the free agent and talks have reached the negotiation stage.
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Il Corriere dello Sport says De Gea is seeking a two-year deal with Fiorentina.
De Gea, 33, has requested a one-year contract with an option for a second, worth €2m net plus €1m in add-ons in the first year rising to €3m plus €1m in add-ons in the second.
The keeper has been a free agent since being released by United a year ago.