Pogba has been holidaying in the US while his agent Mino Raiola tried to broker a world-record 100 million pound move for the France midfielder from Juventus to United.
On Friday, United manager Jose Mourinho had said that the English Premier League club was trying "everything to close the market as quickly as possible."
The 2016-17 season of the Serie A -- the top division of Italian football -- will begin a week after the EPL starts on August 20, with United taking on West Ham United at the Olympic Stadium in London on Sunday.
However, if Allegri's latest comments are anything to go by, the chances of Pogba moving to Old Trafford does not seem too bright at the moment.
"I've summoned Pogba together with (Patrice) Evra tomorrow night. So that means he has training here in Vinovo on Monday," Allegri was quoted as saying by Sky Sports on Saturday when asked if he had identified transfer targets to replace Pogba in the Juventus squad.
"It makes no sense at the moment talking about potential replacements for Pogba because, right now, Pogba is a Juventus player," he added.
"Mourinho rightly says he's not talking about Pogba because he's a Juventus player."
Mourinho has so far signed defender Eric Bailly from Villarreal, midfielder Henrikh Mkhitaryan from Borussia Dortmund and former Paris Saint-Germain striker Zlatan Ibrahimovic.
Pogba left United for Juventus in 2012 as a 19-year-old and has been extremely successful with the reigning Italian champions. The Turin based club has won the Serie A title for five consecutive times starting from 2011-12 season with Pogba a part of four of those campaigns.
The 23-year-old has scored 28 times in his 124 appearances for Juventus.
Pogba's absence from the United squad to face West Ham on Sunday means the seven midfielders available to Mourinho are Miralem Pjanic, Hernanes, Mario Lemina, Kwadwo Asamoah, Roberto Pereyra, Roman Macek and Grigoris Kastanos.
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