The Oscar winner portrays Gianni's sister in the FX mini-series, and ahead of presenting with her co-stars at Sunday's 75th Annual Golden Globe Awards, she shared with ET's Nancy O'Dell how she became involved in the project and how Donatella felt about being depicted on the small screen.
"When [ACS creator] Ryan [Murphy] told me, I said to him, 'This sounds really interesting, but I have to make this call and I have to talk to Donatella,'" she recalled. "I called her and we spoke, like, for an hour. I needed that conversation to say yes."
Cruz insists that she and Donatella have no bad blood between them. "It was a conversation where, I cannot share everything we talked about, but we have a good relationship," she disclosed. "She just sent me flowers before I came here."
Doting on the 62-year-old fashion icon, the 43-year-old actress added, "She's such a loving person, so I wanted to put out there the love and respect I have for her. It's in my performance for sure, and I hope that when she sees, she will be happy about it."
While Cruz feels confident in her portrayal of Donatella, the Versace family told ET in a statement that they do not see the mini-series as an accurate account of Gianni's life or his murder in 1997. They also do not endorse Maureen Orth's book, Vulgar Favors: Andrew Cunanan, Gianni Versace, and the Largest Failed Manhunt in U. S. History, which is the inspiration behind the mini-series.
"The Versace family has neither authorized nor had any involvement whatsoever in the forthcoming TV series about the death of Mr. Gianni Versace," reads the statement. "Since Versace did not authorize the book on which it is partly based nor has it taken part in the writing of the screenplay, this TV series should only be considered as a work of fiction."
During the Golden Globes, ET also caught up with Darren Criss -- who portrays Gianni's murderer, Andrew Cunanan -- and he admitted that he didn't have a lot to work off of when cultivating his character.
"Unfortunately, there's not a whole lot of material on him, so it gives me a lot of leeway to try and fill in the dots myself," the 30-year-old actor said. "I guess the pressure is more to remain sensitive to the people whose lives are still affected by this 20 years later. So, we think about them and we try to shed some light on things that ...a spotlight hadn't been on before. Hopefully we can do the victims a bit of due justice."