On Saturday, the Red Devils are said to have finally reached an agreement with Bayern over deals for both players, with De Ligt set to cost the English side €45m (£38.5m) plus €5m (£4.3m) in add-ons.
Meanwhile, Mazraoui is set to arrive for €15m (£12.9m) plus €5m (£4.3m) in add-ons, with both players said to have agreed five-year contracts at Old Trafford, plus the option of an additional 12 months.
According to transfer expert Fabrizio Romano, Man United are planning to announce both deals on Monday, with the pair now preparing to undergo medicals before the moves are confirmed.
Neither De Ligt nor Mazraoui were used off the Bayern bench in Saturday's pre-season friendly against Tottenham Hotspur - a clear indication that transfers away from the Allanz Arena had been agreed.
Man United 'on verge' of confirming De Ligt, Mazraoui deals
"No, I can't," Ten Hag said when asked if he could confirm the double arrival following Saturday's penalty-shootout loss to Manchester City in the Community Shield. "When we have some news, we will announce it. Until that point, we will work with the squad that is available.
"It's clear we have the problems (in defence) and we have to work. The players have to work to be available and the staff have to work. Together it should be a good collaboration with the players who are available."
Man United were missing Tyrell Malacia, Victor Lindelof and Leny Yoro on Saturday, while Aaron Wan-Bissaka was not involved, as he nears a switch to West Ham United.
Mazraoui will boost Ten Hag's full-back options, while De Ligt is a vital signing in the middle of the defence, with Yoro missing until November due to a foot problem.
When could De Ligt, Mazraoui make their Man United debuts?
In theory, both players should be available for Man United's Premier League opener against Fulham on Friday night, although it would be a surprise if either of them started.
De Ligt was in the Netherlands squad for Euro 2024, but he did not play a single minute for his country, instead being an unused substitute in all six of their games at the tournament.
Mazraoui has had a free summer, but both players are lacking match fitness, so it is more likely that the pair will be on the bench for the contest with Fulham, depending on the team's injury situation.
Luke Shaw could play despite missing the Community Shield, with Diogo Dalot set to operate at right-back, and Lisandro Martinez and Harry Maguire could then feature in the middle for the team's opening Premier League match of the 2024-25 campaign.