The Reds have been in contact with the Vienna club and have communicated that they want 'bring him back now'.
Manuel Ortlechner, director of sports at Austria Vienna, said to Sky Austria: “We are in close contact - I have a phone call (with) Liverpool later.
"They would like to bring Koumetio back."
Speaking more generally about the player, Ortlechner said he believes Koumetio can have a 'really exciting' career beyond Die Veilchen.
“We still think this is an incredibly exciting player," said the club's chief. "He can have a really exciting career, but Liverpool want to bring him back now. They have the right.
“We still have to clarify everything in the end, but we're 99% (certain) Billy Koumetio will no longer play for Austria Wien.”
Liverpool will be looking to bounce back in the FA Cup this weekend after suffering a shock defeat to Brentford in the Premier League.
Perhaps more damaging for the Reds than the result was Virgil van Dijk being hooked off at half-time with his ankle tightly wrapped up.