The 25-year-old is back at Old Trafford this summer after spending the second half of the 2021-22 campaign on loan at Everton.
Van de Beek is believed to be in the plans of Ten Hag for the new season, with the Netherlands international impressing under the club's new head coach for Ajax.
The midfielder has made 50 appearances for the Red Devils since his arrival in September 2020 but has only contributed two goals and two assists during an underwhelming spell.
Ten Hag has said that he views the Dutchman as a number 10, suggesting that he will have to compete with Bruno Fernandes for a spot in the XI during the 2021-22 season.
"He can do both. I know that from the past. But his best position, his best capability is in the box of the opponent. Playing short behind the striker, he has a really good smell of being in the right position," Ten Hag told reporters.
Van de Beek also recently said that he is "really happy to be back" at Man United, and he is targeting "as many minutes" possible during the new season.
"[United] is a massive club with a lot of fans and, to wear the shirt, it's always a special feeling," Van de Beek told the club's official website. "For me as well, I'm really happy to be back. For my experience, I think [the Everton loan] was good. Obviously, I was a little bit unlucky with my injuries.
"I missed a lot of games but to have that experience... it was not an easy season for the team, because we played to avoid relegation, which is not what you want for a club like Everton, but, overall, it was a good experience to be there.
"I think making as many minutes personally, as I can (his aims for new season). I think we need to improve as a team. If you're looking at last season, we have a lot of things to improve. If we work on that now, then we'll see where we end up. We will fight for everything."
Man United opened their pre-season with a 4-0 victory over Liverpool on Tuesday, with Van de Beek playing the whole second half of the clash with Jurgen Klopp's side.
The Red Devils are next in action against Melbourne Victory on Friday, and Ten Hag has said that it will be "a good test" for the club against A-League Men outfit.
"We are happy with this game because it is different opposition. It is always good to play against different opposition, with different culture and it will be a different approach. From Liverpool, Crystal Palace and Aston Villa, we know what we can expect," he added.
"From Melbourne Victory, it will be different. I think they play in a good level and they are second in the league last year so they will have a strong squad and also I think the coach is familiar with top football. So we are looking forward to this game, it's going to be a good test."
Man United will also face Crystal Palace and Aston Villa in Australia before returning to Europe to take on Atletico Madrid and Rayo Vallecano in friendlies ahead of the 2022-23 campaign.