The Reds' defence has once again come in for criticism this season, with many believing it is not up to the standard required for a top-four challenge.
Recent weeks have seen them improve though, with Mamadou Sakho and Dejan Lovren proving the heroes in the 4-3 win over Borussia Dortmund in the Europa League.
Le Tissier though believes that they are still not good enough and it is the one area Klopp must look to improve in the summer transfer window.
“There’s definitely some investment needed at the back,” he told Soccer Saturday.
“I don’t think over the course of a season, looking at Lovren and Sakho, that those two could be the centre-backs that would take you to a Premier League title."
Given Klopp has already moved to secure Schalke defender Joel Matip for next season, it certainly seems he is aware of the frailties in Liverpool's defence.
While the focus is currently on central defence, the left back position must also be of concern to him.
Alberto Moreno has been something of a disappointment since his arrival from Sevilla, and is yet to seriously improve under the German as several of his teammates have noticeably done.