Calzona's Slovakia are in Pot 3 for the draw, ranked above defending champions Italy in Pot 4, but he would prefer not to be drawn in the same group as Luciano Spalletti's side, a coach he has previously worked under.
"I would like to avoid Italy in the group stages, they're a strong opponent and led by one of the best coaches in the world," Calzona told Reuters.
"Maybe after the first round, that would mean that we have achieved another feat."
The Italian has already defied expectations by taking Slovakia to the Euro finals. He took over in 2022, towards the end of a Nations League campaign which saw them finish third in their League C group.
"Putting together 25-30 players from at least 11 or 12 different championships with different roles and mentalities was the hardest part," Calzona explained.
"Getting them to all to think along the same lines, and in a short time was really difficult."
In a Euro qualifying group containing Portugal, Luxembourg, Iceland, Bosnia & Herzegovina and Liechtenstein, Slovakia finished second, five points ahead of Luxembourg, losing just two games, with both defeats coming against Portugal.
"There was great chemistry between all the components, the federation, the staff and the players, we made a single block with the aim of overturning the predictions that didn't see us as favourites," Calzona said.
"I'm very happy, obviously, but I'm happy most of all for the Slovakian people and the federation."
Calzona's achievement is all the more remarkable as this is his first role as a manager, having spent his career as an assistant.
He worked with Maurizio Sarri at eight different clubs, including Empoli and Napoli, and Calzona returned to Napoli in 2021 as assistant to current Italy manager Spalletti.
Calzona was happy to be back at Napoli, but when Slovakia came calling he decided it was time to take the risk of going it alone.
"I love difficult challenges, the comfort zone is not for me. I like to feel the adrenaline, I couldn't know how it would go, but it was worth it," the 55-year-old said.
The opportunity to manage Slovakia came through a former Napoli player, Marek Hamsik, with the country's most-capped player and all-time top scorer suggesting his name to the federation.
"Marek phoned asking me if I was interested in an interview with the federation. He put me in touch with them, we met, we talked and got to know each other, then I was offered the contract.
"Napoli was my comfort zone, where I was respected by everyone and I didn't want for anything, but, as I said before, I like challenges."
This will be Slovakia's third consecutive appearance at the Euro finals, and Calzona's next challenge is to try to reach the knockout stages as they did in 2016.
"The only thing I can say is that we will always play to win, then if this doesn't happen it will only be because the opponents will be better than us," the Italian said.
It's been a long, unlikely journey for Calzona, from his time as a coffee salesman 20 years ago to becoming an international football manager.
"It's been fascinating, that period made me understand many things, it was a fantastic experience that I remember very willingly," he said.
"Still some customers call me asking for coffee."
