“He basically said, ‘I don't want free movement of people but I want the single market,'” Calenda told Bloomberg News. “I said, ‘no way.' He said, ‘you'll sell less prosecco.'
"I said, ‘OK, you'll sell less fish and chips, but I'll sell less prosecco to one country and you'll sell less to 27 countries.' Putting things on this level is a bit insulting.”
Calenda also criticized the chaotic nature of Brexit negotiations and urged the UK to "sit down and put its cards on the table".
The debate comes amid fallout from a leaked memo claiming the UK government had "no clear strategy" over Brexit due to infighting within the Conservative party. Prime Minister Theresa May has said the memo, issued by consultancy firm Deloitte, was not authorized by the government.
Brits are the biggest consumers of Italian prosecco worldwide, having overtaken the US earlier this year, and before the UK referendum winemakers expressed fears that Brexit could cause problems for sales of the Italian fizz.
However, along with other EU countries, Italy has been clear that the UK will not receive special treatment in negotiations. This means that staying in the single market while putting restrictions on the free movement of people - one of the Leave campaigners' main promises - would not be possible.
Prime minister Matteo Renzi said that the UK should not expect more rights than other non-EU countries when it leaves the bloc.
Sergio Gilotta, a professor in business law at Bologna University, told The Local: "EU leaders may well be tempted to 'make an example' of Brexit, showing how hard life will be for those who choose to leave."
"However, both parties have a strong interest in maintaining free trade. Significant trade restrictions with the UK – even the prospect thereof – may adversely affect our economy."
The EU has said that no new relationship can be negotiated until the terms of Britain's exit have been agreed.