Maguire lost his place in the starting team last season and this summer was stripped of the captaincy, which has been given to midfielder Bruno Fernandes.
West Ham had a £20 million ($25.7m) offer for the England international rejected last week, ESPN reported, while there is also interest from Tottenham. But Ten Hag said it is up to Maguire to decide whether he wants to fight for his place.
"Exactly," said Ten Hag when asked whether the decision to stay or go rests with Maguire.
"When you are at Man United you have to fight for your position and bring your skills in and prove you are the best for the team, and contribute the most."
Maguire has been United captain since his arrival from Leicester City in 2019 and retained the captaincy last season in Ten Hag's first campaign in charge.
The Dutch coach insists his decision was nothing personal against Maguire and suggested he wants him to stay.
"It's nothing against Harry, it was in advantage of the team," said Ten Hag.
"Then you make the decision. But I will not say that Harry isn't part of this group. He has to fight for his position.
"He is a very good centre-back, and I believe in the potential of Harry Maguire. It's just that he has to prove himself and fight his way into the team. It's up to him, and I think he can do it."
Maguire made just eight Premier League starts last season and England manager Gareth Southgate has suggested the 30-year-old will have to play more regularly if he wants to keep his place in the national team.
But despite an endorsement of his qualities, Ten Hag has hinted Maguire will again find opportunities hard to come by next season as he battles with Raphaël Varane, Lisandro Martínez, Victor Lindelöf and Luke Shaw.
"It's tough when you're competing with Rapha Varane and Victor Lindelof," Ten Hag said.
"It's huge competition. That has nothing to do with the belief. I have often chosen a player ahead of Harry, that's true. But that says nothing about me not believing in him. He has to show he is better for the team than Rapha or Victor. I think that's a normal situation in top football."