Di Marzio claims the Premier League threw out the bid on Monday night.
Pogba's agent Mino Riola is extremely keen on the move as he will pocket 20% of his client's transfer fees again and Pogba also wants to move to the better opportunity at Barcelona.
The 25-year-old midfielder had an indifferent season at Old Trafford last term, with reports of a falling out with boss Jose Mourinho.
Pogba, who did not accompany United on the US tour, will meet Mourinho this week after returning to United's Carrington training centre Monday after a three-week break following France's World Cup triumph. Reportedly, the French star is miffed with United manager Mourinho.
The Spanish transfer window closes on 31st August but the Premier League deadline is Thursday, leaving United little time to replace star man Pogba should Barcelona get their man.
And Pogba's impressive World Cup appears to have caught the eye of one of Europe's biggest clubs.
According to rumours, Pogba has desired to join Barcelona but a chance of a reunion with Juventus will be quite tempting for him.
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The fractured nature of Pogba's relationship with Mourinho will give Barcelona hope that a deal can be struck.
Dembele also fuelled speculation over a potential move to the Gunners after he had dinner with several Arsenal players last week, including Pierre-Emerick Aubameyang and Henrikh Mkhitaryan.
United executive vice-chairman Ed Woodward is naturally understood to be unwilling to sell club-record signing Pogba - a stance backed by former defender Rio Ferdinand, just as a move for Alderweireld would be.
Manchester United are not interested though, in letting the midfielder leave.
United begin their league campaign on Friday evening against Leicester City.