The Liverpool Echo says Karius is expected to arrive in the Turkish capital on Friday to undergo a medical ahead of a two-year loan switch.
And as Karius moves ever closer to the Anfield exit door, it looks like Besiktas supporters are going to see their social media perseverance pay off.
The fans of the Turkish Super Lig club are known to be some of the most passionate around and they have inundated Karius' social media channels since Besiktas' interest was revealed earlier this month.
Karius' uploads on Twitter and Instagram have been met by thousands of comments from Besiktas followers urging him to join their club before the August 31 deadline.
The most recent upload attracted an eye-watering 231,000 comments, the majority of which were from Turkish fans keen to see the Liverpool goalkeeper join their team.