The Italy striker is on-loan at Lazio from Atalanta, having arrived in January.
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The deal includes a €14m option, which Lazio now intend to take up, says Il Corriere della Sera.
Lazio coach Maurizio Sarri is delighted with Maldini, who is playing as a No10, rather than on a flank, where his long-term position was expected to be.
Instead, Sarri is playing Maldini centrally and behind the centre-forward and has been impressed by the youngster's efforts.