The Dutchman scored only three Premier League goals in his first season at Old Trafford, and could have been sold if manager Ruben Amorim was more ruthless in the transfer market.
Manchester United has spent around £130 million on new attacking players this summer, including Bryan Mbeumo and Matheus Cunha. However, Zirkzee is not fazed by the competition and wants to see the team improve on the pitch.
"I am very confident. We have competition, and I will play in any position the coach needs me to," Zirkzee said.
"The coach knows me well, and I have 100 percent trust in him. I am not worried about competition," he added.
Zirkzee suffered a hamstring injury in April that kept him out for almost the rest of the season. Many people criticized him, but he believes that his age and inexperience in the Premier League contributed to his poor form.
He admits that his lowest point last season was when he was booed by his own fans at Old Trafford in January, but he is not selfish and only wants to see the team improve.
"Cunha and Mbeumo are great players, and we are all about the team. We want the team to be good," Zirkzee said.
"Everything is for the team, not for individual players. If it helps the team, then great," he added.