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Leoni will join be part of the squad alongside Virgil van Dijk, Ibrahima Konate and Joe Gomez, who has returned to training this week.
Liverpool are also trying to sign Crystal Palace defender Marc Guehi and are continuing talks with their Premier League counterparts for a deal of around £35m.
He can play in the middle of a back three or on the right side of a two.
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Liverpool’s sporting director Richard Hughes remains in talks with Parma chief executive, Federico Cherubini but the main parts of the deal are agreed.
The deal does not make any difference to Liverpool’s pursuit of Guehi with talks to continue through this week.
Guehi, 25, has just one year left on his contract at Selhurst Park and wants to make the move to Anfield.
Liverpool want to do a deal this summer but could take him for free in 12 months.
Marc Guehi could leave the Eagles this summer(Image: Clive Mason/Getty Images)
Palace chairman Steve Parish does not want to let Guehi go for free but also wants over £40m for him with negotiations to continue.
Palace turned down a £70m bid from Newcastle in January and went on to win the FA Cup.
They have been demoted to the Conference League but they are still set for a big season and would want to replace Guehi if he departs so want to command as high a fee as possible.
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