Chief executive Ivan Gazidis says Arsenal need to be "open-minded" in finding a new manager following the announcement of Arsene Wenger's departure.
Wenger is to stand down at the end of the season after a reign of almost 22 years and while Gazidis refused to discuss whether the Frenchman left entirely of his own accord, he said the search for a new manager had not yet begun.
"The most important thing is to make the right appointment - not a quick one," said Gazidis, who said that out of respect for Wenger no discussions had been held while he was in the post.
"The process begins today. I want to keep that process in-house. This club has to rise to the challenge. You don't find a replacement for Arsene Wenger, you find a new path forward.
"We need to be open-minded and also brave in the decision. Be bold and get the person we believe is the right person."
Former AC Milan and Chelsea manager Carlo Ancelotti, Atletico Madrid's Diego Simeone, Massimiliano Allegri of Juventus, Germany coach Joachim Low and former Arsenal midfielder Patrick Vieira are among the names mentioned as possible replacements.
Gazidis gave few clues about the profile of manager the club would be looking for but suggested they would have to be adept at bringing through young players and adhere to Arsenal's values.
"Our academy teams are doing extremely well. Under the radar, we have a lot of young players coming through so that value of bringing in youth has got to be one," Gazidis said.
"When Arsene was appointed, he was not on everyone's radar. What I will say is that it's important to me that we continue the football values that Arsene has instilled at the club.
"Someone who plays exciting and progressive football. But I think there is also a significant thing at Arsenal in how the candidate represents the club. We need to make sure we don't lose his qualities and his values."
Gazidis said the Frenchman would always have a place at the club but said it was "too soon to say how that would look".
He also suggested Wenger might not be ready to retire from the game just yet.
"He's somebody who is in great shape and has a competitive edge but that's a question for him," he said.
The Arsenal CEO said the timing of the announcement would allow the club's fans to give Wenger a strong send-off.