The champions were handed a major blow at the weekend when Van Dijk hobbled off the Merseyside derby with a serious knee injury.
The defender is now tipped to miss the entire season and it has been claimed that the injury is worse than feared and extends beyond just a cruciate ligament injury.
Liverpool have been reduced to two senior centre-backs in Joel Matip and Joe Gomez, with Fabinho also equipped to play at the back.
There has been a growing expectation that Liverpool will have to dip into the transfer market in January after losing Van Dijk.
However, Liverpool have yet to discuss signing a centre-back and will not be rushed into a decision.
Jurgen Klopp will assess his options over the next two months and may opt to work with the players he has at his disposal, rather than making a signing.
Liverpool looked at a number of centre-backs over the recent transfer window, but chose not to replace Dejan Lovren.
