Koeman, who was appointed last August on a two-year contract, has had to manage the fallout from Lionel Messi's ultimately unsuccessful transfer request ahead of the 2020-21 campaign.
Uruguayan Araujo, who has played in 15 LaLiga games this season after featuring in just six during his debut campaign in 2019-20, has been impressed with Koeman's efforts and wants him to remain at the helm beyond this season.
"It's very good that the board has confidence in Koeman because the boss has shown that he is a great coach," the 22-year-old told TV3.
"He is very good with the team and the locker room. This relationship is very important. I am very happy that he can continue with us because he brings a lot to us, especially the young people.
"The work he had in front of him was not at all easy, considering how the whole situation was. But he is a coach with a lot of character, who knows how to deal with these issues, and the coaching staff have done a very good job.
"We are working well and that translates into the way the locker room is and the results."
Araujo also declared his admiration for Messi and hopes Barca's talisman stays at Camp Nou beyond this season.
On Sunday, Messi overtook Xavi as the player with the most appearances for Barca (768), six days after the 33-year-old scored a 20th LaLiga goal for the 13th successive season – another record.
The Argentina forward has been involved in more goals in 2021 than any other player across Europe's 'top five' leagues, but he still has not tied his future to the Catalan club, with Manchester City and Paris Saint-Germain reportedly interested in signing him.
"I hope he stays with us next year and many more years to come," Araujo added. "Leo is fine, I see him very happy. He works a lot, not only in matches, but also in training.
"Messi trains like a beast and that's very good because he is the captain and he is a reference, and he spreads it to us all, to the rest of the team and to the young people."