The Daily Star says Chilean media sources are reporting a deal has been struck for the 27-year-old, with United ready to offer £32m and Patrice Evra in order to get their man.
Vidal's performances for his country at the World Cup caught the attention of a host of European clubs.
However, United appear to have jumped ahead of the pack.
Juve are keen to bring veteran Frenchman Evra to Turin this summer, and the player is also keen on a switch to Italy.
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