One of Buongiorno or Mancini is expected to be named in Luciano Spalletti's starting lineup alongside central defender Alessandro Bastoni, as Riccardo Calafiori is serving a one-match suspension.
Torino's Buongiorno was only handed his senior international debut this time last year and the four-cap centre-back is now in contention to start for his country at a major tournament for the first time.
The 25-year-old has admitted that he has been working hard in training since arriving in Germany to give Spalletti a 'selection headache' and believes he is well-prepared should he be called upon to start on Saturday.
Speaking at a press conference, Buongiorno said: "There's enthusiasm (in the squad). From the start of the camp, we've been trying to give our all to give the coach a selection choice headache. If it were to be my time, I've prepared to be ready."
Buongiorno: 'I've shown my strong points to Spalletti'
"I try to put the effort in and improve day after day, setting goals to improve my shortcomings. I believe I have shown my strong points are in the defensive side of the game, and also with Spalletti we are working hard on my skills in the possession phase; that is where I feel I need to improve further.
"In every training session, the coach gets his ideas across to us: I believe very much in his football and in what he tells us; they are all very useful and will allow us to improve individually as well as a team."
Buongiorno added: "This part of the draw seems simpler, but every match is tough. We will try to do our best and hope to succeed for us, for Italy, and for all Italians".
Meanwhile, Roma defender Mancini has earned 12 caps for Italy since and including his debut in 2019 and has suggested that every defensive option at Spalletti's disposal, including himself, is capable of filling in for the suspended Calafiori.
"I am not the youngest but Bastoni and Calafiori are playing and doing very well," said Mancini. "Then Buongiorno, Gatti and I are there to be ready when the coach calls on us or when we have to get involved. We are a cohesive and compact group".
Mancini talks up "very physical" Switzerland clash
Talking up the qualities of goalkeeper and captain Gianluigi Donnarumma, Mancini added: "We all know Gigio. He has been one of the best goalkeepers in the world for a few years, he's proving this and having him behind us is a big help, you see that on the pitch".
Mancini is expecting a "top-level game" against a "very physical" Switzerland side, who finished second in Group A behind Euro 2024 hosts Germany.
"We saw Switzerland against Germany (a 1-1 draw on matchday three), they are a very physical side, fast and run a lot," said the 28-year-old. "It will be a top-level game and we will try to get the best out of it. They have both young and expert players, it's a good mix, a side with big names and other younger players who have the skill to do well.
"But our side too has a good mix of experience and youth. Many players have played or currently play in the Italian league. It will be an open game given that some of us know each other, others less so, but it is important to focus on ourselves and do things well to win the game".
Italy, who finished second in Group B behind Spain after collecting four points from three group games, head into Saturday's contest having drawn six of their last eight meetings with Switzerland.