Mr Ciobo wouldn't divulge the specifics of his conversation with Dr Fox, but said there was a "lighthearted reference" to the serious matter.
"Notwithstanding that it has been the butt of a number of jokes, the fact does remain that this actually does go to reputational injury and we need to be mindful of that," he said.
"Cricket Australia …. recognises that so after undertaking due process I do believe they're going to take the appropriate action."
The comments come following a weekend that for Australian officials at least, was supposed to be about the launch of a new Perth-London direct flight from Qantas and ahead of a key speech on the importance of free trade delivered at Bloomberg's new European headquarters in London designed to spruik Australia's $27 billion trading relationship with the UK.
However the cricket scandal has dominated front and back newspaper pages in England and led to a comment from Prime Minister Theresa May whose spokesman said she was "shocked" and "bitterly disappointed" by the events.
"The Prime Minister is clear that cheating has absolutely no place in cricket or indeed in any sport," the spokesman said.
"The Australian Prime Minister Malcolm Turnbull has said that cricket fans will be shocked and bitterly disappointed by the news, and the Prime Minister agrees with that."
Qantas boss Alan Joyce, who had recently travelled to London on the 17-hour non-stop flight, said the airline was "in discussions" with Cricket Australia about its sponsorship role.
"We are very disappointed. Australia is all about 'fair go', and I think all Australians are very disappointed with what's happened with the cricket team."
"We've let them know that we want them [the authorities] to urgently complete the investigation and take the appropriate action," he said.
High Commissioner to UK Alexander Downer also told the BBC he was "outraged" when he heard the news and "punishment is certainly justified"
"The national team for Australias is iconic and for them to behave in this way is just unbelievable.
"It is bad for the national psyche ... For people wearing the baggy green to be behaving like that is just astonishing ... The team has lost the affection and support of the public."
COUNTING THE COST
The reputational damage comes amid reports the scandal could cost Cricket Australia the $1 billion it expected to rake in over the years ahead for television rights to the game.
Deakin University sports management lecturer Michael Naraine told the ABC it was "hard to put a dollar figure" on the damage but Cricket Australia could give up hopes of a $1 billion bill for rights.
"They're not going to get that, and I think it's probably going to be closer to the $600-700 million mark," he said.
The Courier Mail also reports "bidding had not reached the heights expected" already due to the "turn-off factor" of some of the players, such as David Warner.
Major sponsors are also reviewing their commitment to the team after the shock admission of ball tampering. Fund Manager Magellan, Weetbix maker Sanitarium, beer and wine distributor Lion and Commonwealth Bank are among those said to be reviewing their options and awaiting the outcome of the sport's leading body.
"We are disappointed about the events that have emerged from the third Test in South Africa and have asked for a full explanation from Cricket Australia following the conclusion of its investigation into this affair," a spokesman for CBA said.
The relationship with Sanitarium is said to be "under review" while celebrity agent Max Markson said individual players will "lose every single one" of their contracts.
Warner's website lists Asics, LG, Gray Nicholls, Nine, Toyota, Nestle's Milo and the Make-a-Wish Foundation as brand partners.
Mr Ciobo is in London to hold talks with UK Secretary of State for Trade Liam Fox and Secretary of State for Environment, Food and Rural Affairs, Michael Gove about a "high quality" free trade deal to be signed once Britain leaves the EU.
