The Australian, who received the World Rugby coach of the year award after taking the Wallabies to the World Cup final, said no one from England had approached him and described coaching Australia as "the dream".
"No one from England has contacted me and they know that they can't contact me because I'm committed to Australia and that's where I want to be coaching," the Telegraph quoted Cheika as saying.
"I'm an Australian coaching Australia, it's like the dream. There's nothing that would make me change my mind."
England's RFU have suggested they want someone of proven international experience, although they have had a tough time attracting interest. Steve Hansen, Graham Henry, Wayne Smith, Warren Gatland and Joe Schmidt have all distanced themselves from the position.
Cheika however suggested that there were "lots of good English coaches who could be coaching England".
"If you look like a guy like Dorian West at Northampton, he's done such a good job with the scrum and forwards. Jim Mallinder, Rob Baxter, Dean Richards - I just think there are a lot of those guys who are typical of the English game and could do a lot for the team."
England next play on February 6 (local time), as they kickoff their Six Nations campaign against Scotland.
