The 22-year-old will be signing for around £8.5 million, with the deal not likely to include any sell-on or buy-back clauses.
Araujo joined Barca in February 2023, but never got the first team game time he expected.
Having played more than 100 times for LA Galaxy, Daily Echo states he will now get a Premier League chance.
Araujo will have his medical on Monday and then could join up in training with his new teammates a day later.
Head coach Andoni Iraola told the Daily Echo: “I think it is true that they (the clubs) are speaking.
“There are talks ongoing. But he is Barca’s player. Until the signing is not done, I cannot consider him our player.
“He played in Galaxy and he played in La Liga last season. But I wasn’t there, so I haven’t see him live.
“But obviously there are a lot of people in the club who travel and see a lot of players a lot of times live and sometimes on video.
“They control the market much better than me.”