The Argentina international was close to signing for the Nerazzurri in the summer of 2012 before he eventually made the move from Napoli to Paris Saint-Germain instead
The 27-year-old was heavily linked with a move to the Giuseppe Meazza side ahead of the 2012-13 campaign but eventually opted to leave Napoli for the French capital instead.
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"Pocho [Lavezzi] was close to joining Inter in the past. They showed an interest in signing him a number of times," Mazzoni told the Corriere dello Sport.
"He never said that he's an AC Milan fan and would never join Inter. He could go to Inter, a team who already have a lot of Argentines.
"He likes the city of Milan because of the high-quality football and it's a place where someone can live in peace.
"Any player who has played in Serie A is interested in a return there. Football in Italy is nothing like in France. PSG are a very important team, though, who will do well next season."
Lavezzi has a contract with the Ligue 1 leaders until June 2016.