The Red Devils have signed Joshua Zirkzee and Leny Yoro this summer, with the former arriving from Bologna, while the latter has made the switch from Lille.
Zirkzee is yet to make his debut for Man United due to his involvement in the Netherlands squad at Euro 2024, and he will not link up with his new teammates until the start of August.
However, Yoro, less than two days after arriving, made his debut as a starter against Rangers.
The centre-back is also with the squad in the United States and is set to be involved in the upcoming matches with Arsenal, Real Betis and Liverpool.
Ten Hag wants more incomings at Man United
Ten Hag has welcomed the two new arrivals but has said that he wants "the squad as strong as possible", insisting that the club "need to catch up" in terms of squad depth.
"I want the squad as strong as possible. We already made two very good buys so when everyone is fit we have a team that can beat everyone. But with squad depth we need to catch up because we had injuries. This season will be survival of the fittest," Ten Hag told reporters.
"We proved we can beat the best team. Not just once, we did it twice. But also the other games were also very close. Our challenge is to do it consistently, that's what we have to work for."
Man United opened their preparations for the new campaign with a 1-0 defeat to Rosenborg, but they bounced back with a 2-0 victory over Rangers last weekend.
The Red Devils will now tackle Arsenal, Real Betis and Liverpool before heading back to England to prepare for the Community Shield against Manchester City on August 10.
Who else could Man United sign this summer?
Man United are said to be pushing to sign Noussair Mazraoui from Bayern Munich, with the Morocco international seen as a potential replacement for Aaron Wan-Bissaka.
West Ham United are allegedly no longer in the race for Mazraoui, with Man United potentially securing a deal in the near future.
The 20-time English champions also want to bring in a central midfielder, with Paris Saint-Germain's Manuel Ugarte viewed as their leading target, but Real Sociedad's Martin Zubimendi and Sporting Lisbon's Morten Hjulmand are also admired.
The Red Devils are also looking to acquire another centre-back, with Matthijs de Ligt the leading target, but any deal for the Bayern defender depends on outgoings, with Victor Lindelof potentially departing to make space for the Netherlands international.