The Gunners have had a relatively quiet summer compared to some of their Premier League rivals, with David Raya being the only confirmed signing so far.
Raya spent last season on loan at the Emirates Stadium from Brentford and completed a permanent move to North London at the start of the month.
The Premier League runners-up have been pursuing the Italian defender for several weeks, navigating tough negotiations with Bologna before finalising an agreement last week.
Arsenal had signalled their interest in the 22-year-old early in the transfer window but discussions only gained momentum after Italy were knocked out of Euro 2024.
'Incoming' - Calafiori to undergo medical today
According to transfer expert Fabrizio Romano, Calafiori is set to make the trip from Italy to London today, and he will undergo the first part of his medical shortly after his arrival.
The report adds that if all goes according to plan, the Italian will then head to the US to join Arsenal in their pre-season tour by this weekend.
When asked about Arsenal's bid to sign Calafiori on Thursday and to provide more details about the transfer, Mikel Arteta had little to share: "There is no update," he said.
"As soon as we have something to say, we will be the first one to say. You know I don't like talking about external players, but this is the situation at the moment."
That interview came after the Gunners' opening pre-season friendly, where they secured a victory over Bournemouth on penalties following a 1-1 draw.
Arteta's side will continue their pre-season tour of the United States with another friendly match against Premier League rivals Manchester United in the early hours of Sunday morning.
Basel set for significant windfall from Calafiori transfer
Bologna paid just £3.4m for Calafiori from Basel, who are believed to have around a 40% sell-on clause on the player, which they negotiated during his move to Italy in 2023.
In his debut season back in his homeland, the 22-year-old featured in 37 matches and contributed to seven goals, scoring two himself and setting up five.
His performances were also instrumental in the club's impressive Serie A campaign, where he helped them secure a spot in the Champions League for the upcoming season.
Calafiori has three years remaining on his contract with Bologna but made it clear to the club's board that he wishes to move to a bigger team this summer.
The arrival of the Italian defender could signal the end for Jakub Kiwior, who has reportedly been told by Arsenal that he is free to move on this summer, with both Milan clubs believed to be interested in his services.