The Bosnia international is under contract with Roma until June 2018 but has a clause in his contract which allows him to leave Roma this summer provided a fee of 38 million euros is paid for his release.
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"Miralem Pjanic undergoes a medical ahead of his proposed move from Roma," Juventus said in a statement.
The 26-year-old, who arrived in Turin on Sunday, joined Roma from Lyon in the summer of 2011.
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He scored 10 goals and set up 12 more in 33 league appearances to help Roma finish third in Serie A this season.
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