Besiktas had changed its Twitter cover photo to one of Karius, in a Besiktas shirt, with the caption 'LORIS KARIUS #COMETOBESIKTAS'.
Later on the club removed the picture of Karius but retained the hashtag and added '#NEWEPISODE Coming Soon...' to the cover photo ahead of an expected announcement.
Karius made two dreadful errors in Liverpool's UEFA Champions League final loss to Real Madrid last May, although tests later revealed he had suffered a concussion during the game. He has subsequently lost his place in the team to Brazil international Alisson.
Karius was then omitted from Liverpool's 18-man squad for its win over Crystal Palace on Tuesday (AEST) amid reports he was on the verge of joining Besiktas on a two-year loan deal.
Speaking just prior to the Turkish club's social-media activity, Liverpool boss Jurgen Klopp had claimed there was "nothing new" on Karius's future.