The Spaniard has been linked with a move away from the Bees throughout the summer after turning down the chance to extend his stay with Thomas Frank's side.
Tottenham Hotspur considered a move for the shot-stopper earlier in the window, but they were put off by Brentford's £40m asking price.
There was also interest from German champions Bayern Munich, who were looking to agree an initial loan deal with an option to sign him on a permanent deal.
Ultimately, a move to the Bundesliga side failed to materialise after talks broke down, paving the way for Arsenal to enter the race.
Arsenal have seemingly identified Raya as someone that can offer competition to the club's current first-choice goalkeeper Aaron Ramsdale.
The Gunners have been locked in talks with the Bees, with a recent report claiming that a deal was close to being agreed.
According to journalist Fabrizio Romano, the Gunners have now wrapped up negotiations and have reached an agreement with Brentford to sign Raya.
The Spain international has already agreed personal terms with Arsenal, and the necessary paperwork is being finalised.
There is an expectation that a medical will take place this week, before Raya is unveiled as Arsenal's latest summer addition.
While Raya is set to complete a move to North London, Ramsdale's current deputy Matt Turner is on the verge of joining Nottingham Forest.
The USA international has reportedly undergone a medical with the Tricky Trees after the two clubs came to terms on a £10m deal, including add-ons.
Icelandic goalkeeper Runar Alex Runarsson is also expected to leave the Emirates Stadium this summer, having spent the last two seasons on loan at Belgium side OH Leuven and Turkish outfit Alanyaspor.
Arsenal will be hoping to announce Raya's arrival before they kick off their Premier League campaign with a home fixture against Forest on Saturday.