Calafiori has played nine games under José Mourinho this term and joins Genoa in a temporary transfer.
“We are happy to welcome a young and talented player such as Calafiori, he will help us with his qualities," said the Rossoblu director Johannes Spors.
The move came about after Ainsley Maitland-Niles arrived from Arsenal on-loan.
Genoa were eliminated from the Coppa Italia Round of 16 on Thursday and sit 19th in the Serie A table, with just one win in 21 matches.
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