Warner was named vice-captain for an Australia A game last month and this week he will lead a Chairman's XI against India.
"Michael's [Clarke] doing a fantastic job at the moment, but you're always looking for leaders within your group and it would be lovely to have 11 people that took leadership qualities on and I think Davey Warner's one of those and that's why he's been given the role to lead this squad," the Sydney Morning Herald quoted Cooley, as saying.
"Dave is really keen, he knows the game, he plays it in an exciting way so I'll be very interested in watching him over the next few days lead this team. I think he's an exciting prospect and he hasn't led teams often, but he has a lot of input into the leadership around the group so it'll be interesting to see how he goes," he added.