There is some speculation such as Barcelona might be targeting Arteta to replace Xavi in the future.
I don't see this very realistic at the moment. Because before anything else, Barcelona management don't seem uncomfortable with Xavi's job right now. Maybe their being eliminated in the Champions League this easy was some loss of credit for Xavi but they are still hopeful about the La Liga title now. This is the most serious season for the title as they can play at a similar level with Real Madrid right now. But if they don't keep up a good form and let Real Madrid pull away earlier then Xavi might be in trouble. Then Arteta might be a choice considering his success with Arsenal so far this season.
https://www.sport.es/en/news/barca/barca-looking-at-mikel-arteta-as-a-future-coaching-option-77972868It depends. Xavi's experience with Barcelona as a coach is quite short and building a team requires a lot of patience. Obviously, repetitive defeats aren't acceptable. I assume he will be forced to leave once Barcelona fails badly in Europa League. They are one of the favourites teams to win it so losing early or badly by big score might affect his future. Winning La Liga in the other hand might save him.
For Arteta, he had many difficulties with Arsenal previously before getting a team that made City suffers to try get the first place.
Mikel Arteta dismissed rumors that he would coach Barcelona, he confirmed that he was happy with the Gunners' young squad. however, if he is going to leave the Emirates Stadium. IMO, most likely he is more suitable to replace Pep Guardiola's role at Manchester City. So far, Pep Guardiola is rumored to be leaving the Premier League after his contract expires with The Citizens. however, it seems Haaland's presence makes Pep will extend his new contract with Haaland's future project.
as for Artera. on several occasions, he delivered. he has big ambitions with Arsenal this season by marrying two Premier League titles and the Europa League.
on the other hand, Xavi's future with Barcelona is reportedly in turmoil after failing to bring Barcelona to the last 16 of the champions league. however, the target has changed. currently, Xavi has stated that he is targeting the Europa League and La Liga trophies. however, if he fails to bring Barcelona to the title this season.
in other words, it is certain that his coaching career with Barcelona will end in dismissal.