Everton are on the hunt for a new man in the dugout after dismissing Rafael Benitez earlier last week.
Rooney had two spells as a player for the Toffees but is now in charge of championship side Derby County, albeit in challenging circumstances.
Derby County are currently embroiled in a relegation battle after being docked points at the start of the season for entering into administration.
Rooney insists he is ready for a challenge as a Premier League manager but wants to focus on his task at Pride Park for now.
"Everton approached my agent and asked me to interview for the vacant job, which I turned down," he said on Friday.
"They got in touch with my agent, my agent let the administrators know as well, and yes of course it was a difficult decision for me [to turn it down].
"I believe I will be a Premier League manager. I believe I'm ready for that, 100 per cent. And if that is with Everton one day in the future, that would be absolutely great. But I've got a job here that I'm doing at Derby County, which is an important job to me."
Everton have reportedly turned their attention towards appointing one of Duncan Ferguson, Frank Lampard or Victor Pereira as their new manager.
