The Gunners have already secured the signatures of Nuno Tavares and Albert Sambi Lokonga in the current transfer window, and 23-year-old White would represent the third youthful incoming of the summer for Mikel Arteta.
White is understood to be keen on a switch to North London, with the Gunners seeing two bids of £40m and £45m knocked back by the Seagulls until their £50m valuation was met, and the centre-back could be announced as an Arsenal player by the end of the month.
With that in mind, Sports Mole looks at which shirt numbers are available to White at the Emirates Stadium.
White was handed the number three jersey for the 2020-21 Brighton season and did the shirt justice under Graham Potter, but the '3' is currently occupied by Kieran Tierney at Arsenal, and the left-back will not be relinquishing that shirt any time soon.
However, the '4' - which White briefly wore during his time in the Seagulls' youth setup - is available following William Saliba's loan move to Marseille, and the Englishman being handed that jersey would be a true indication of how highly Arteta rates him.
White would have some big boots to fill if he does sport the '4', though, as Arsenal icons such as Tony Adams, Patrick Vieira, Martin Keown and Frank McLintock have all donned the jersey down the years.
The '8' is also free following Dani Ceballos's return to Real Madrid, but even though White has been utilised in midfield under Potter, it would be a shock to see the versatile centre-back handed that shirt.
White was trusted with the famous '5' during his successful loan spell at Leeds United, but that number has been taken by Thomas Partey for the new season, while the '6' - which he has worn for England, Peterborough United and Notts County - is in the possession of his expected centre-back partner Gabriel Magalhaes.
The defender's late call-up to the England squad for Euro 2020 saw him handed the number 22 jersey - a shirt that has been worn by some of Arsenal's less impressive performers such as Yaya Sanogo and Denis Suarez - but Pablo Mari currently holds that jersey in North London.
The '28' has also been sported by White during his early days as a senior Brighton player, and while that shirt currently belongs to Joe Willock at Arsenal, it could be freed up if the midfielder completes another move to Newcastle United.
Only one jersey between 36 and 99 is occupied at Arsenal right now - with goalkeeper Dejan Iliev donning the 52 - but Arteta is not expected to hand White such a high number as he hopes to establish himself as an Arsenal regular.