The Gunners have agreed a £50m fee with the Seagulls for the 23-year-old, who is set to undergo a medical this weekend.
However, Arsenal will need to raise funds from player sales in order to balance their books, and according to The Mirror, Mikel Arteta is wiling to let as many as seven players leave the club this summer.
Arsenal's longest-serving player and vice-captain Hector Bellerin is another who could move on, as the right-back is seeking a fresh challenge away from the Emirates, with Inter Milan the current frontrunners for his signature.
In addition, funds could also be raised from the potential sales of Alexandre Lacazette, Willian, Sead Kolasinac, Lucas Torreira and Joe Willock, who are all unlikely to receive regular first-team football next season.
Arsenal have already been busy this summer in the transfer market, following the arrivals of Benfica full-back Nuno Tavares and Anderlecht midfielder Albert Sambi Lokonga for a combined £22m. body check tags ::