The Gunners are confident the 25-year-old wants to join them but Brentford are reluctant to part with Raya as they seek promotion to the Premier League after losing the 2019-20 Championship playoff final to Fulham.
They are under no financial pressure to sell but could find an improved Arsenal bid difficult to resist given the player's desire to leave.
Arsenal sold back-up goalkeeper Emiliano Martinez to Aston Villa on Wednesday for £20m and are seeking to reinvest some of those funds by signing two replacements with a deal to sign Iceland international Runar Alex Runarsson from Dijon close to completion.
That would allow third-choice goalkeeper Matt Macey to leave, although there are no formal offers on the table.
Bernd Leno has been told he will be Arsenal's No. 1 this season and so the club must weigh up whether to invest more money in acquiring Raya, given the need to strengthen other areas of the first team.
First-team manager Mikel Arteta wants to sign Houssem Aouar from Lyon and Atletico Madrid's Thomas Partey but both players would command significant fees and Arsenal need to offload several fringe players before they can make further signings.