Monk, who managed to convince the youngster to give up on Under-19s European Championships this summer in order to concentrate on pre-season, is hopeful that Cook will be playing at Elland Road next season.
"It was a very difficult decision for myself," Monk told Leeds' official website.
"I spoke to Lewis and told him how important he is to this team and for the project going forward.
"I just felt that to miss him for pretty much the whole of pre-season would be detrimental to the player and detrimental to myself and the team.
"I took the decision. Talking to the player, I made him very aware of the reasons why and he fully understood.
"I spoke to Aidy Boothroyd, the manager of England for his age group, and he understood. Of course, they wanted Lewis to be there with them but it's a decision that I've had to take.
"I'll play the villain in this but it was for the right reasons – England understand that and Lewis understands that. I think it's what's best for us going forward."