The Serie A champions are prepared to lose Paulo Dybala, Mario Mandzukic and Blaise Matuidi in order to re-sign their former midfielder.
However, United had previously failed to convince Dybala to move to Old Trafford in a separate proposal involving Romelu Lukaku.
It remains to be seen whether the Argentine will lower his wage demands in the final days of the English transfer window, but Juve hope that their proposed swap deal will persuade United to let Pogba go.
The France midfielder excelled in four seasons with the Bianconeri, who he joined after leaving United on a free transfer in 2012.
And Juventus are so determined to bring him back to Turin that they are willing to offer three first-team players to Ole Gunnar Solskjaer's side.
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