Jose Mourinho said he hoped to have his Manchester United squad "closed" by next week while also appearing to take another swipe at Arsene Wenger for speaking out during the transfer window.
Paul Pogba's transfer saga has dragged on despite multiple reports this week the deal is moving closer to completion.
Mourinho has said his team is missing one more piece in the midfield, though he declined on Wednesday to identify Pogba, and took the same tack in a news conference on Friday.
"I don't like to speak about other players. Other managers like to do that," Mourinho said. "What matters to me is only what happens in my house, not the house of my neighbour.
"Pogba is a Juventus player until officially he isn't. It stays like this."
But with one week to go before the start of the Premier League season, the manager did provide a timeline for the deal to possibly be completed.
"Honestly, the market closes on Aug. 31, but I think my club is trying to do everything to close our market before Aug. 14," he said. "So hopefully be next week we will have our squad closed."
Mourinho has had a fraught relationship with counterpart Wenger in the past, describing the Frenchman as a "specialist in failure" in 2014.
And the Portuguese issued another veiled shot at his rival after the Arsenal boss labelled Pogba's expected £100 million transfer fee "completely crazy," and called other team's spending "scary."
"There are things that when I do [them], it is not ethical but when others do, nobody says that and everything is normal," Mourinho said.
"But the reality is I don't speak about the others. They can do what they want."
Mourinho has already made three additions in his first summer at Old Trafford, signing defender Eric Bailly, midfielder Henrikh Mkhitaryan and striker Zlatan Ibrahimovic, and the manager remained confident that the final piece would fall into place.
"We got a young central defender that needs time to be a top one, but he has top potential and we believe a lot in him," Mourinho said. "We brought Micki here, a player that we know the quality he has.
"We got a super striker [in Zlatan] and we are going to get a very good midfield player, so I am happy with the balance of my squad, I'm happy with the effort that the club has, and is still putting in for us."
Even if Pogba does join up this month he is unlikely to be fully fit following an extended holiday in the United States, and Mourinho said the rest of his players have varying levels of fitness depending on when they rejoined the club.
"One thing is to start five weeks ago, like some of them, and another thing is to start one week ago -- it is completely different," he said. "But the way we work we try to bring them on as fast as we can.
"I won't say to top form but to a level where they are ready to compete. That is the reality of modern football."
The manager also said Chris Smalling and Tim Fosu-Mensah are "fine" despite neither featuring in preseason games to this point.