The 34-year-old’s contract with the reigning European champions runs out in the summer, and his agent has confirmed that he is unlikely to pen a new deal.
And Pirlo, who was allowed to leave Milan on a free transfer before helping Juve to last season's Serie A title, has expressed disbelief at the Blues' failure to tie Lampard down.
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"Lampard could have another four years at the top in Italy. If he wants to play in Italy I would welcome him to Juventus with open arms.”
The Chelsea vice-captain joined the club from West Ham for £11m in 2001, and has netted 193 times in 576 appearances since.
Lampard has earned Champions League, Premier League, FA Cup and League Cup winners’ medals during his time in west London.