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Rabiot will see his contract with PSG expire at the end of this month and is therefore available on a free transfer.
United reportedly approached the midfielder with the offer of a lucrative contract last week.
However, according to Italian journalist Gianluca Di Marzio, Rabiot has turned down the chance to move to Old Trafford to instead agree a long-term contract with Juve.
The 24-year-old has made 227 appearances for PSG in all competitions, winning five Ligue 1 trophies during his time in Paris. However, the Frenchman has not represented Thomas Tuchel's side since December.
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