Sportmediaset says Sir Alex Ferguson oversaw the offer during his visit to Turin last week for the Europa League final.
Ferguson was there to see Sevilla win the final, but also on official United business as he made an offer of €32 million for Chile international Vidal.
The United director is close to Vidal's agent, Fernando Fecelivich, and rates Chilean players highly.
It's claimed, however, that United's offer was thrown out by Juve, which won't do business for less than €40 million.
For the big stories and the banter follow us on Twitter: @tribalfootball