According to the Express, who have cited 'reports in Spain', Alonso wants to move into management but wants coaching experience first in order to earn his coaching badges.
Arteta and Alonso have been friends since childhood, having grown up together in San Sebastian before playing alongside each other for amateur side Atiguoko.
The duo never played together professionally as they went their separate ways. Arteta moved to Barcelona while Alonso signed for Real Sociedad.
"I follow him very closely because we have kept in touch forever, from when he move from Everton to Arsenal," Alonso said of Arteta when speaking to Arsenal's YouTube channel in 2016, also per the Express. "I want to know how it works there in Arsenal, and he’s enjoying it so far."
Arteta is set to join the club as manager after gaining experience as Pep Guardiola's assistant at Manchester City since 2017.
City boss Guardiola has said that he doesn't want Arteta to leave, but would not stand in the 36-year-old's way if he wants to move on to progress his career.
“We were together so good, all the staff, Mikel," said Guardiola. "So if he stays I will be happiest guy in the world. If he decide to move because he has this offer, this option, I will not say you don’t have to go. I want the best for my friends, and he’s a friend of mine, and I want the best.
“If he decides to go, I will be so sad, but I will understand his decision, because it’s his career, his life, his family, and I am not right guy to say you don’t have to do that. But hopefully he can stay and finish what we have started together in the coming years.”
Meanwhile, another player linked to the assistant manager role is Santi Cazorla. The Spaniard hasn't featured at all for Arsenal since 2016, due to several complications that hampered his recovery from a long-term injury.