The Reds have been constantly criticised for the amount and type of cheap goals they have conceded this year.
That was none more so evident than during the 3-3 draw with Arsenal on Friday.
Liverpool squandered a 2-0 lead to finish the game level and it was again the defending which came into question.
But at forefront of the blame is goalkeeper Simon Mignolet, who should have done better to save Granit Xhaka’s effort.
And now with the transfer market opening in eight days’ time, Murphy wants to see Klopp bring in a new number one.
“We know that Liverpool need a new goalkeeper,” Murphy told Match of the Day.
“As for Mignolet we have said enough over the recent months.
“Week in week out, although we see brilliant Liverpool, we see Liverpool who do not defend.”
However, at the top end of the pitch Liverpool continue to impress with the forward four of Philippe Coutinho, Roberto Firmino, Sadio Mane and Mohamed Salah proving almost unstoppable.
And Murphy wants to see the Reds shore up the defence so the forwards can continue to shine.
“They should have had the game won,” Murphy added.
“They played brilliantly going forward.
“You have got to keep the lead, you have done the hard work.”