And bookmakers Paddy Power have been forced to slash their odds for the title from 10/3 to 3/1 after a flurry of bets.
United were as long as 13/2 at the end of May but are now second favourites behind Manchester City at 23/10.
Chelsea and Arsenal are both 6/1 while last season's champions Leicester are priced at 22/1.
Pogba's move to United would make him the most expensive player in history and he would follow Eric Bailly, Zlatan Ibrahimovic and Henrikh Mkhitaryan in Jose Mourinho's overhaul.
The 23-year-old France star left United in 2012 for free but has developed into one of the top players in the game.
He said "We know the profile of the player we want and have three players to fit that profile.
"I am really confident Ed Woodward (United's executive vice chairman) will get the profile of the player because the squad needs balance."
Asked specifically if a deal with Pogba is close to being agreed, he added: "I don't confirm and I don't deny. I cannot tell.
GETTY
Manchester United's title odds have been slashed with Paul Pogba's imminent move
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"First of all, because I don't think it’s correct to speak about players from other clubs. He's a Juventus player, not a Manchester United player.
"The only thing I can say is that my board, my directors, did fantastic work to do 75 per cent of the job I asked them to do.
"I asked them for four profiles of players, I gave them a few options and they did for me 75 per cent of the job in (Zlatan) Ibrahimovic, (Henrikh) Mkhitaryan and (Eric) Bailly, and we just have 25 per cent to do before August 31.
"So we are in a great conditions to do what I consider will be a great market for us. So we are calm."