Talks are ongoing but Brighton are standing by their valuation of £50m for the 23-year-old, who was a surprise inclusion in Gareth Southgate's England squad for Euro 2020.
White is thought to be open on a move but Arsenal could face competition from several Premier League rivals for his signature amid speculation Liverpool, Tottenham and Manchester United are interested.
Arsenal boss Mikel Arteta is looking to overhaul his squad after finishing eighth last season, their lowest placing since 1995. Arsenal have already an offer for midfielder Albert Sambi Lokonga dismissed by Anderlecht, who want €20m to complete a deal.
Arsenal are looking to offload several other players, however, as they need to bolster their transfer funds through player departures with Matteo Guendouzi in talks to join Marseille. Greek defender Konstantinos Mavropanos will also be allowed to depart.