Monk was unveiled as the club's new manager on Monday and was introduced to the media at Rockliffe by CEO Neil Bausor.
Questions were asked about the future of Steve Agnew, who replaced Aitor Karanka at the helm in March, and the composition of the football staff, who will be working alongside the new manager.
"We'll work with Garry over the coming days to piece together that support staff," said Bausor.
"Steve Agnew has been fantastic and has been a great servant to this club over a number of years.
"We hold him in the utmost respect and will be talking to him in the coming days about what his future is."