Elsewhere on the third day at the All England Club, four-time major winner Naomi Osaka targets back-to-back wins at the tournament for the first time since 2018.
Italian men's tennis has rarely been stronger, with the country boasting five players in the top 50 while the nation swept to Davis Cup glory last season.
Ten Italian men started the singles tournament this year at Wimbledon.
Sinner was the first Italian man to capture a Grand Slam title with his victory at the Australian Open in January and was also the first from his country to become world number one.
"I feel like in Italy we have so many tournaments, starting with juniors, then the Futures and Challengers," said 22-year-old Sinner.
"We have big, big ATP tournaments there. We have good facilities and great coaches."
Berrettini can boast his own breakthrough Italian moment when he was the first to make a Wimbledon men's final in 2021, where his run was ended by Novak Djokovic.
Sinner, who made the semi-finals at the All England Club last year, defeated Berrettini in their only previous meeting at the Masters-level event in Canada last year.
"I think his secret is that he is really hungry for improvement. That's his secret. And the humbleness that he has about it. He's just special," said Berrettini of his compatriot.
'Destroying the ball'
Third-ranked Alcaraz is bidding to become just the sixth man after Rod Laver, Bjorn Borg, Roger Federer, Rafael Nadal and Djokovic to win the French Open and Wimbledon titles back to back.
He defeated dreadlocked Estonian qualifier Mark Lajal in the first round as he started his bid for a fourth Grand Slam title after adding last year's Wimbledon to his 2022 US Open breakthrough.
On Wednesday, he faces Aleksandar Vukic who enjoyed an impressive run to the semi-finals of the Eastbourne grass-court tournament last week.
The 28-year-old Australian, ranked at 69 in the world, was born in Sydney after his parents fled Montenegro during the break-up of Yugoslavia in the 1990s.
He booked his date with Alcaraz the hard way, saving a match point in a five-set triumph over Sebastian Ofner, facing down 24 aces and 72 winners from the Austrian.
Vukic can boast one career win over Alcaraz -- he came out on top against the then 17-year-old Spaniard in the first round of qualifying for the 2020 French Open.
"You could tell he was going to be special. There was a lot of hype around him," recalled Vukic.
"He was destroying the ball. It was obvious something was going to happen. I think two years after that he was World No. 1. It is just a crazy rise."
'Fun, stressful'
Osaka defeated Diane Parry of France in the first round to register her first win at Wimbledon since 2018.
Former world number one Osaka, still feeling her way back on tour after giving birth to daughter Shai last July, fired 34 winners past Parry on a surface that should be the perfect fit for her powerful game.
"It felt really fun and really stressful at the same time," said 113th-ranked Osaka, whose last appearance at Wimbledon in 2019 had ended in a first round exit.
The Japanese star takes on America's 17th-ranked Emma Navarro, who arrived in London on the back of a semi-final run at the Bad Homburg grass-court tournament.
Navarro has high achievement in the genes -- her father Ben Navarro is a former vice-president of banking giant Citigroup.
Forbes recently estimated his worth at $1.5 billion.
Three-time Grand Slam title winner Stan Wawrinka and Gael Monfils face-off in a match featuring two men with a combined age of 77.
It will be the third oldest combined age in the Open Era.
There could be a memorable day for Chinese tennis with teenager Shang Juncheng taking on 10th-seeded Grigor Dimitrov and 32nd seed Zhang Zhizhen facing Germany's Jan-Lennard Struff.
Until Monday, no Chinese man had won a match at Wimbledon in the Open era.
Rain, however, could be the spoilsport after the start of play on the outside courts was delayed by over an hour.
