The former England and Manchester United captain had two spells with his boyhood club Everton as a player.
However, the lure of a return to Goodison Park was not enough for Rooney to give up on the challenge of keeping the Rams in the second tier of English football despite a 21-point deduction due to financial problems.
Derby are second bottom of the Championship, but just eight points adrift of safety.
“Everton approached my agent and asked me to interview for the vacant job, which I turned down,” Rooney told a press conference.
“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.”
Derby went into administration in September and there remain fears the club may not have the funds to fulfil their fixtures for the rest of the season.
On Thursday, the English Football League (EFL) handed the club’s administrators a one-month extension to be able to provide proof of funding.
Rooney’s reluctance to return to Everton is also a reflection on the state of affairs at the Premier League club.
The Toffees are four points clear of the relegation zone after a dismal run of just one win in 14 league games.
Rafael Benitez, who had been a deeply unpopular appointment due to his history as a former Liverpool manager, was sacked by Everton earlier this month.
Fans protested after last weekend’s 1-0 home defeat to Aston Villa and throughout this week outside Goodison Park.
Rooney’s former England team-mate Frank Lampard is now the leading candidate for the job after supporters voiced their opposition to the prospect of Vitor Pereira taking over.
Pereira has won league titles in Portugal, Greece and China, but he is deemed a risky appointment given his lack of experience in English football.
Objections to Pereira’s appointment are also rooted in resentment at agent Kia Joorabchian’s reported influence on key decisions made by Everton owner Farhad Moshiri.
“I think these critics are not directed at me. It is the environment now as the club is not in a good position and the supporters are passionate,” Pereira told Sky Sports.
“But I understand the feelings of the supporters because, in the last few years, the club didn’t get good results and it is normal they are not happy.”