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The 41-year-old coach enjoyed a positive 2016/17 season, guiding Lazio to fifth in Serie A and the Italian Cup final, which they lost to Juventus, meaning they will play in next season's Europa League.
Inzaghi, a former Italy international forward and brother of World Cup winning striker Pippo, took over first team duties at Lazio at the end of the 2015/16 season, having previously coached the youth team.