All three were involved in Euro 2024, but McTominay's Scotland failed to make it through the group stage, while Hojlund and Eriksen's Denmark were beaten by Germany in the round of 16.
McTominay will return to training on Wednesday and could potentially be involved in the team's second pre-season friendly of the summer against Rangers on Saturday.
Meanwhile, Hojlund and Eriksen are set to return next week, with the pair due to travel with the first-team squad to the United States for the club's pre-season tour despite being involved in the knockout round of Euro 2024.
"It starts on Wednesday with Scott returning," Ten Hag told reporters on Monday. "Then, next week, Rasmus Hojlund and Christian Eriksen are returning, then they go on the tour."
Man United opened their pre-season with a defeat
Man United started their preparations for the 2024-25 campaign with a 1-0 defeat to Rosenborg on Monday night, but it was a youthful squad that made the trip to Norway.
Marcus Rashford, Casemiro, Aaron Wan-Bissaka, Jonny Evans and Mason Mount were the five senior players involved, with the likes of Harry Maguire, Antony, Amad Diallo, Victor Lindelof and Andre Onana staying in Manchester.
Altay Bayindir, Diogo Dalot, Bruno Fernandes, Kobbie Mainoo and Luke Shaw were all involved in the latter stages of Euro 2024 for their respective countries and are not close to returning to the squad.
Meanwhile, Lisandro Martinez, Facundo Pellistri and Alejandro Garnacho turned out at the Copa America.
New signing Joshua Zirkzee was a late call-up to the Netherlands squad for Euro 2024, and he is not expected to be available until the start of next month.
Ten Hag talks-up Zirkzee potential
"He is a player who can link up the game," Ten Hag added when asked about the forward. "Who can be available, hold up the ball, have good ideas, be creative, can dribble, [make] combinations.
"So that's a different type and always what we are looking for, so it gives us more options tactically, which is good because, especially up front, we have many players who can play very direct and they can take a big benefit from his skills."
Zirkzee is Man United's first signing of the INEOS era, but the club are expected to bring in at least three more players before the summer transfer window closes.
A deal for Bayern Munich's Matthijs de Ligt is advancing, while the Red Devils are also still working on moves for both Lille's Leny Yoro and Everton's Jarrad Branthwaite.