Cocu was dismissed earlier this week with Derby bottom of the Championship table, having won just once from 11 attempts this season.
Rooney, who joined Derby earlier this year as a player-manager, is one of four coaches placed in interim charge of the Rams for the short-term as the club searches for a new manager.
Rooney’s first game in interim charge will be at Bristol City on Saturday and the 35-year-old former Manchester United and England captain is eager to follow in the footsteps of former teammates Frank Lampard, Steven Gerrard and Scott Parker in becoming his own boss.
“I wouldn't be an ambitious person if I sat here and said I didn't want the job,” Rooney told a press conference.
“We all come into this game to play football and then you have a decision to make: do you want to go into coaching or management?
“I've made it quite clear over the last few years that my ambition is to go into management, especially when you see the likes of Steven Gerrard (Rangers), Frank Lampard (Chelsea) and Scott Parker (Fulham) all getting good jobs and doing really well at it.
“We have to get the next two or three games out the way first, but if they go well it puts me in a better position to put our names forward for that role.”
“I have worked with some very good managers and possibly the greatest of all time,” he added. “I am not going to say I am going to do it like Sir Alex Ferguson. You have to work with the players you have got and you have to manage players correctly.
“There is an opportunity to show the different ideas that you have. But there are things you can take from other managers.”
Derby are in the middle of a takeover by Abu Dhabi royal family member Sheikh Khaled bin Zayed Al Nehayan, who is the cousin of Manchester City owner Sheikh Mansour.
