The Gunners have been strongly linked with a move for their former captain, who made 149 appearances in five years at the Emirates Stadium.
Arteta has been a crucial part of Guardiola's extensive backroom team as City have set new records for Premier League points, wins and goals this season.
Guardiola made it clear that he wants Arteta to stay with the champions, but won't resent it if he decides to move into management as Arsene Wenger's successor.
“We were together so good, all the staff, Mikel," said Guardiola, quoted by the Sun. "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.
Arsenal not close to appointing new manager. No agreement yet on chosen candidate, negotiations at relatively early stage, thorough process ongoing, next week looks unrealistic. Once decided, IG/RS/SM will present recommendation to #AFC board. Arteta among names being considered— David Ornstein (@bbcsport_david) May 12, 2018
“But hopefully he can stay and finish what we have started together in the coming years.”
Arteta is one of two ex-Arsenal captains to be strongly linked with the Gunners job, along with New York City head coach Patrick Vieira.
Vieira was the initial favourite to succeed Wenger but Arteta has now emerged as a serious contender for the job and is the favourite with many bookmakers, along with Juventus manager Max Allegri.
Allegri appeared to rule out a move after Juve won the Serie A title on Sunday, telling the media: "If they don't fire me, then I think I'm staying."