The Mirror reports as things stand, a permanent move is yet to materialise.
Karius has been photographed at Liverpool's pre-season training camp in Austria this week, an unfamiliar face after so long away.
With Euro 2020 over and done with and transfer business well underway, Karius will have to hope that someone tables a suitable offer.
At 28, he can ill-afford to spend a season as fourth choice behind Alisson, Adrian and Caoimhin Kelleher, with youngsters Marcelo Pitaluga and Harvey Davies also pushing for a back-up role.
The German spent last season on-loan with Union Berlin.
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