The former Napoli captain is free agent after ending his three-year spell with Toronto FC.
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His former Napoli coach, Maurizio Sarri, is in regular contact about a move to Lazio in the New Year.
However, Sky Deutschland's Florian Plettenberg is reporting: "34 y/o Lorenzo Insigne is planning a return to Europe.
"After three years with FC Toronto in Canada, he is now without a club and keeping himself fit.
"He would like to play in Serie A once more, but he is also open to other leagues. The Bundesliga is an option for the European champion as well, and he is prepared to accept significant salary reductions."