"If we deserved the sentence, there would be nothing to say," Stefano said on Wednesday.
"But we do not deserve it, and so unfortunately we would have to close."
CLICK ON PHOTO TO VIEW FULL GALLERY
"We will close. What do you want us to do?" Said Domenico. "We will close. We will not be able to deal with it. [It would be] Impossible."
"We are not going to give in to being crucified like thieves, because we are not," added Stefano.
"How could we accept being branded tax evaders? We are good people, we live in Italy we pay taxes in Italy, we don't pretend to live abroad."
Despite denying accusations that they sold their brand to a Luxembourg-based holding company in 2004 to avoid declaring taxes on royalties, Domenico and Stefano lost their case in March 2012 and were sentenced to one year and eight months in prison.
The pair were also ordered to pay the €343million fine when they were found guilty. The Milan Courts of Appeal ruled that the fashion designers had failed to pay around €1billion in taxes and ordered them to pay the substantial fine on 30 March 2012.
The case dates back to an investigation that began in 2007, when authorities clamped down on tax avoidance after the financial crisis had set in.
Charges were brought against the designers, and five other individuals, after their two brands, Dolce & Gabbana and D&G, were sold to Gado Srl. The Guardia di Finanza believed that Gado was a legal body set up up to enable the pair to avoid the country's high corporate taxes.
It meant that profits from the two labels were taxed abroad and not in Italy, where authorities believed Dolce & Gabbana and D&G were still being managed from.
In April 2011, Judge Simone Luerto dismissed charges against them as unsubstantiated. But in November 2011, the Supreme Court of Cassation overturned the ruling and ordered a retrial saying, "tax avoidance, or tax mitigation on an earnings declaration is a criminal offense under the law".