Milenkovic was signed by Corvino for the Viola in 2017, arriving from Partizan Belgrade for €4.59m. The defender, now 23, is a first-choice for Fiorentina and Serbia and has a contract with the Viola to 2022.
Corvino, now in charge of Lecce, admits United made an attempt for the defender when he was still working for the Florence club.
The Serb is again being linked with United this summer, while European champions Chelsea are also reportedly eyeing the stopper. This past season, Milenkovic played 37 games for Fiorentina, scoring three goals.
Corvino also recalled signing Dusan Vlahovic, who like Milenkovic joined Fiorentina from Partizan Belgrade.
He continued: "For (Dusan) Vlahovic, on the other hand, I scared my club when in 2017, for a 2000 non-EU boy who was not yet eligible for membership, I paid 1.5 million euros in advance to Partizan to close immediately.
"At the time of the signing, Vlahovic's father told me: 'Director, I'm sure you are bringing the new (Gabriel) Batistuta to Florence'. Addressing his mother too, I replied: 'Well, I was convinced instead of having brought home a new Luca Toni'. There was a general laugh."
Vlahovic scored 21 goals in 40 games for the Viola last season. The 21 year-old has a deal with Fiorentina to 2023.
- updated June 22