Sources have told ESPN FC that United are interested in central defenders Jerome Boateng, Toby Alderweireld, Harry Maguire and Yerry Mina but Mourinho - who has said the season could be "difficult" if the squad is not bolstered - admitted at a news conference on Thursday he is not expecting any new arrivals.
It was also a good day for Leicester City, who, not only managed to keep hold of Harry Maguire amid reported interest from United, but also brought in the well-regarded young defender Caglar Soyuncu from Freiburg, tied Jamie Vardy down to a new deal and signed Croatia Under-21 global Filip Benkovic.
He was also, however, firm in his stance that his old club Manchester United "should be challenging" regardless of their inability to add a top quality centre back to their side during the transfer window.
United finished as runners-up last season, 19 points behind Manchester City, and Mourinho has already made it clear that his team needs more players if they are to overhaul their neighbours.
Asked if nothing would happen in or out before the Premier League deadline at 5pm, he said: "The information I have is no (nothing will happen)".
Mourinho revealed he will be without six senior players for the game against Leicester.
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He said that he believes Liverpool will finish ahead of Manchester United in second place and Tottenham Hotspur will finish fourth despite a summer in which Mauricio Pochettino's team did not spend a penny in the transfer market. Premier League came out of his mouth before we'd even finished the question.
"Is hard for me to understand, to feel, to believe we finish second - which I keep saying, and it is sometimes hard to believe, that I won eight championships and three Premier League's but I keep feeling the second last season was one of my biggest achievements in the game".
"Because it is very important how they feel and to understand how they think they can help or not help". In football you need time to work and players on the pitch to work and we didn't have that until now.
"It looked like I was saying something absolutely out of order, something insane, I repeat: Pre-season hard when you don't have your players to work, that's as simple as that". I was told that during pre-season it looked like I was saying something absolutely out of order, something insane.