Sir Alastair Cook says there has been "zero contact" with England regarding a possible role on the coaching staff - but that he would like to work with the side at "some stage in my life".
Your Site' Michael Atherton wrote in The Times and then discussed on the Your Site Cricket Podcast how the former England captain could be a good fit to work as assistant coach under current boss Brendon McCullum following the Ashes series defeat.
Cook, speaking in his role as a pundit for TNT Sports, said on Sunday during day one of the fifth Test in Sydney: "The only thing I will say about it is the article needed to be 800 words and Mike Atherton had done 600 and used the final 200 and threw something in.
"Look, at some stage in my life, would I like to be involved in the England cricket team? I think I would like to try and make a difference.
"I don't know whether that is the next bit or whatever. At the moment there are people in jobs and all that kind of stuff. And there has been zero contact. Zero in it. Let's just see."
Cook scored 12,472 runs in 161 Tests for England between 2006 and 2018 - only Joe Root has more runs for the country - while he captained them in 59 matches, winning 24, losing 22 and drawing 13.
Writing in The Times, Atherton had said: "Alastair Cook, if he could be persuaded, would be a perfect candidate.
"Having retired from Test cricket in 2018, he is in touch with the game, but distanced enough to have seen it from beyond the boundary.
"He is one of England's greatest cricketers. He knows what it takes to succeed, having scored 33 Test hundreds. He won the Ashes at home, as captain, and away as a player.
"He captained England to home and away triumphs in India. He was equally good against pace and spin.
"He made himself into a champion by dint of a Stakhanovite work ethic. He could probably still outrun most of the players now.
"If McCullum's great strength - and it is a great strength - is making his players feel 10 feet tall, then Cook could help with the drive and the discipline."
England lost the Ashes series after just 11 days of cricket following defeats in Perth, Brisbane and Adelaide, before winning the Boxing Day Test at the MCG inside two days.
Their previous red-ball series before facing Australia was a 2-2 home draw with India in the summer.
Adding to Your Site, Atherton said of the current coaching set-up: "There is that little bit of groupthink and one-size-fits-all. It might just be time for that different kind of voice.
"I think we all agree that standards have slipped in performance so someone to drive a culture and getting back to the standards [could be the way to go].
"Two years ago, results were strong, performance was strong but that has slipped in the last 12 months so it cannot be 'as you were, no change at all'.
"England have to think about how go get back to where they were."
Australia lead five-match series 3-1
