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The reports said the 29-year-old would sign a three-year contract with the 29-times Italian champions. Juventus did not immediately comment.
Gazzetta dello Sport, Sky Sports Italia, Tuttosport and Corriere dello Sport all said an agreement had been reached following a meeting between officials from the clubs in Manchester, with Juventus expected to pay €12 million.
Tevez spent four years at Manchester City after joining them from neighbours United, but it was far from plain sailing.
Although he won a Premiership winner's media in 2011/12, he was also fined and suspended by City after refusing to warm up during a Champions League match at Bayern Munich in 2011.
He has also fallen out of favour with the Argentine national side.
His signing would mark a change in direction by Juventus, who have won the Serie A twice in a row without a big name forward.
Coach Antonio Conte has rotated between any two of Sebastian Giovinco, Alessandro Matri, Mirko Vucinic and Fabio Quagliarella, who have shared the goals evenly between them.
Tevez began his career at Boca Juniors in Argentina and has also played for Corinthians in Brazil and West Ham United in England.
He has never been far from controversy and was once sent off for Boca after celebrating a goal against River Plate by flapping his arms to imitate a chicken, a reference to that fact Boca fans use "chickens" as a derogatory nickname for their arch-rivals.
