Negotiations have intensified this week after Vidal's agent, Fernando Felicevich, met with United manager Louis van Gaal on Monday.
Chile's La Tercera says United have tabled a bid of £40 million plus Javier Hernandez in exchange for Vidal.
The midfielder has already agreed personal terms with United over a deal settled some weeks ago.
Van Gaal will insist on a stringent medical for Vidal, who went into the summer's World Cup with a knee injury.
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