The goalkeeper recently started the second season of a two-year loan spell with Turkish club Besiktas.
Ally McCoist pays tribute to Rangers legend Fernando Ricksen
Karius left Liverpool last summer following his error-strewn display in their Champions League final defeat to Real Madrid and the £67million arrival of new no.1 Alisson.
When quizzed about his Merseyside future, Karius said: “I’m not thinking about it at the moment.
“There’s still a long way to go before my loan spell ends.
“I am focusing on matches, my performances. We will talk about it at the end of the season.”
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Karius has been Besiktas’ first-choice glovesman since joining, though it took him quite a while to impress with a series of dodgy displays characterising his early spell in Turkey.
And he made another calamitous mistake in the Turkish club’s 4-2 Europa League defeat by Slovan Bratislava on Thursday.
Karius needlessly rushed off his line and misjudged the flight of the ball, which allowed Andraz Sporar to pass into an empty net.
Besiktas manager Abdullah Avci slammed his side’s individual errors following the Europa League defeat.
He said: “At this level, we cannot make such individual errors.