Karius was preferred to Mignolet as Liverpool's number one last season, but the summer arrival of Alisson Becker - which was sparked by high-profile errors from Karius in the Champions League final - knocked both players down the pecking order.
Mignolet had been expected to leave the club rather than stay as third choice, but Liverpool instead sent Karius out on a two-year loan to Besiktas, with an obligation to make it permanent should certain criteria be met.
The Belgian described the decision as "bizarre" but insists that he still wants to leave Anfield in search of more regular first-team football.
"The transfer of Karius doesn't change anything for me. I have always been clear: I want to play," he told Het Laatste Nieuws.
"Being number two or number three makes little difference. Playing minutes is the most important thing. Nobody has said anything to me after the departure of Loris. So I don't know what my future at Liverpool is. We will see what happens this week.
"I find it bizarre that Karius was loaned while I also had options to be loaned. But for some reason that was not possible. A goalkeeper who was preferred to me last year may leave on a loan basis. Strange."
Mignolet has been on the bench for Liverpool's last two Premier League games.