Speaking to the media ahead of Liverpool's Premier League opener against Bournemouth, the manager revealed a deal had been struck between the two clubs.
"The clubs have agreed a deal, but he has not signed for us yet," Slot said.
"The moment he does, I can go into more detail."
Leoni is a highly-rated defender who has already featured 17 times in Serie A for Parma, aged just 18.
The Italian would arrive to help fill a hole in Liverpool's defence despite his young age - although the Reds are reportedly still pushing to sign Crystal Palace's Marc Guehi.
Slot was coy on any links to the Englishman, as he has been throughout the window so far.
"He (Guehi) is not our player. If you want to have any talks about him, go to Palace."
Leoni would be Liverpool's seventh signing of a busy summer so far at Anfield.