The Reds have already signed Steven Caulker from QPR on loan.
The Reds have struggled at the back this season, with the likes of Martin Skrtel, Mamadou Sakho, Dejan Lovren and Kolo Toure all failing to impress at the heart of the defence.
Similarly, they are currently short on numbers, with a series of injuries having robbed manager Jurgen Klopp of several of his stars in defence.
The German has already moved to improve that situation by bringing Steven Caulker in on loan from QPR, but Murphy expects more movement, saying improving the defence will be his priority in the January transfer window.
“Liverpool have a few injuries at the back, notably to Dejan Lovren and Martin Skrtel, but even when that duo are fit the middle of their defence looks vulnerable,” he told BBC Sport.
“Klopp has already signed centre-back Steven Caulker on loan and brought goalkeeper Danny Ward back to the club from Aberdeen.”
“And that is where I think he will be looking to add players this month, not in positions up the field where he already has plenty of options.”
The problem for Liverpool is whether they will be able to secure the type of players that Klopp would want in the January transfer window.
The winter window is notoriously difficult to do business in, with clubs unwilling to sell their star players unless they can do so for often over inflated prices.
Indeed, it seems Klopp has already accepted it may be difficult to secure who he wants, with the capture of Caulker looking more like a move to add bodies than bring in a player they were desperate to sign.