The Scotland international was persistently linked with a move to the Emirates Stadium during his time at Bologna, whom he joined from boyhood club Hearts in 2020.
While plying his trade in Serie A, Hickey established a reputation as one of Europe's most promising up-and-coming full-backs, scoring five goals and setting up one more in 48 games.
Amid widespread interest in his signature, Brentford won the race to bring Hickey to the Premier League in a £14.4m deal, and the 21-year-old set up one goal in five top-flight outings during his debut campaign.
So far this term, Hickey has started all six of Brentford's games in the Premier League, alternating between left-back and right-back roles, and his contract with Thomas Frank's side is due to run until 2026.
The 6ft 1in defender has also become an integral member of Steve Clarke's Scotland setup since making his debut last March, and he has started all five of their Euro 2024 qualifying wins from a wing-back role.
Frank affirmed earlier this year that Brentford have no intention of letting Hickey leave, but according to The Mirror, three members of the Big Six are ready to test the Bees' resolve.
All of Arsenal, Liverpool and Man United are believed to be weighing up bids for the Scotland international, who has also attracted glances from German champions Bayern Munich.
However, Brentford are expected to hold out for a proposal worth at least £50m before entertaining the idea of a sale, especially with Rico Henry set to miss the rest of the 2023-24 season with a knee injury.
Nevertheless, the Premier League trio all have reason to pursue a deal for Hickey, who would fit Arteta's criteria as a versatile defender capable of starring on either flank.
The Gunners offloaded Hickey's compatriot Kieran Tierney to Real Sociedad on loan this summer, while Cedric Soares is down the pecking order and expected to leave when his deal runs out in 2024.
Meanwhile, a hamstring injury to Trent Alexander-Arnold has left Liverpool short of right-back options, leading to Joe Gomez and Stefan Bajcetic filling in on that side since the international break.
The Reds loaned Calvin Ramsay to Preston North End this summer, but the Scotsman is set to miss the first two months of the season due to a setback in his recovery from surgery.
Over at Old Trafford, Man United struck a loan deal for Tottenham Hotspur left-back Sergio Reguilon, but all of Aaron Wan-Bissaka, Tyrell Malacia and Luke Shaw are sidelined with injuries.
The full-backs have now been joined in the infirmary by Lisandro Martinez, who missed Saturday's 1-0 win over Burnley owing to an unspecified issue of his own.