Xhaka is said to be angry that Arteta has praised him publicly, while contradicting that in private, report Blick.
Arteta is already said to have held talks with the player prior to the Bournemouth clash, where he allegedly told Xhaka he's happy for him to leave the club.
"That's the way it is," said Xhaka's agent José Noguera.
Now Xhaka looks set to depart in January, and already has a destination in mind.
Noguera added: "We are in agreement with Hertha Berlin and [Xhaka] would like to go. So we told [Arsenal's Head of Football] Raul Sanllehi and sports director Edu - as well as the new coach Mikel Arteta.
"Granit would like to switch to Germany again."
Hertha are said to have tabled a bid worth around £21 million - although Arsenal are likely to want to hold out for more.