The Italy Under-19s centre-back began his career at Padova and had a short spell at Sampdoria before joining Parma last summer.
Leoni played 17 games in his first campaign in Serie A last season, attracting interest from both Milan clubs, but has opted for a move abroad.
Liverpool have been looking for reinforcements in central defence since selling Jarell Quansah to Bayer Leverkusen last month, with Crystal Palace's Marc Guehi also linked with a move to Anfield.
Leoni's transfer is subject to receiving international clearance and a work permit.
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