"I think that as Borussia we're also allowed to think big and try things that might not seem feasible at first glance," Schröder told Bild.
He stressed that speed was less important than finding the right fit for the club.
"What matters in the end is that we find the right coach for Borussia, and it doesn't come down to a single day.
"It's about the coach fitting with us, knowing the league and our squad, and having an idea of what's possible and how to get more out of it."
Asked specifically about Domenico Tedesco, recently sacked by Bologna, Schröder did not rule out an approach.
"These days the average tenure is around a year, so you always have to look at each individual case. I don't choose a coach based on whether he's been at the same club for six or nine years," he said.
Tedesco had already been on Borussia Monchengladbach's radar once before, when the club ultimately opted for Eugen Polanski, who has since also been dismissed after a poor start to the season. Whether the former Leipzig and RB Salzburg coach gets a second look this time around remains to be seen, but Schröder's comments suggest no candidate is being ruled out purely on reputation or salary grounds as the club works through its search for a long-term appointment.
Schröder himself only took charge of Gladbach's sporting operations recently, arriving from Red Bull Salzburg to succeed Roland Virkus at a club that has struggled for form and stability over the past year.
The coaching search represents his first major test in the role, coming just months after he oversaw the appointment and swift dismissal of Polanski, a decision that has already drawn criticism from sections of the German media. A swift and successful resolution to the current search would go some way to easing the pressure building on Schröder himself as he looks to stabilise the club both on and off the pitch.