Milan are moving for Lavezzi after being frustrated in their pursuit of Hellas Verona ace Juan Manuel Iturbe, who is in talks with Juventus.
Sportitalia says Lavezzi is currently in Paris discussing a new deal with PSG. However, he is aware of Milan's interest and not ruling out a return to Italy.
The former Napoli star has been a regular visitor to Milan since leaving for France over two years ago.
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