The Swiss midfielder, who has been stripped of the Gunners captaincy, said he "can't accept" what has gone on.
Xhaka scored in Switzerland's 6-1 win over Gibraltar on Monday that sent them to the Euro 2020 finals.
He told Swiss broadcaster SRF: "I have a clear idea as to how things should proceed, and Arsenal know this as well.
"Although I still have a contract with them, I will be glad to return to the club - so we can finally sort matters out.
"There will surely be a solution - as I can't accept what has happened with me."