England failed to progress beyond the group stages of the World Cup on home soil and coach Stuart Lancaster left the post by mutual consent last week.
Cheika led the Wallabies to the World Cup final at Twickenham where they lost 34-17 to New Zealand on 31 October.
"I'm an Australian coaching Australia. It's the dream. There is nothing that would change my mind," Cheika said.
Speaking to BBC Radio 5 live, he added: "No-one has contacted me, and they know they can't contact me because I'm committed to Australia."
Cheika was only appointed Australia coach in October 2014 and in a year turned a side then in disarray into World Cup finalists.
The 48-year-old coached Leinster to the Heineken Cup title in 2009 and has also been in charge of French club Stade Francais and Australian state side NSW Waratahs.
