The Reds were linked with Netherlands international Van Dijk throughout the summer transfer window but Liverpool couldn’t get a deal over the line.
The Merseyside outfit were forced to issue an apology for their pursuit of Van Dijk, officially pulling out of the race for the defender.
However, Liverpool continued to be linked with the Southampton captain despite their earlier statement amid reports the Dutch star preferred a move to Anfield.
But transfer deadline day passed and Liverpool failed to land the 26-year-old, forcing Klopp to rely on Dejan Lovren and Ragnar Kalgan alongside Joel Matip.
Former Manchester United defender Neville questioned why Liverpool didn’t do everything possible to get a deal over the line.
“They’ve got problems at centre half. There were problems with Southampton so I’m not sure they would have done a deal. It was still an area of the team that I felt needed strengthening,” Neville told BBC Radio 5 Live.
The Reds slumped to a 1-1 draw with Burnley at Anfield on Saturday afternoon after Mohamed Salah equalised for the hosts.
Van Dijk moved to Southampton from Scottish champions Celtic in 2015.
Liverpool signed four players in the summer transfer window, including Hull City defender Andy Robertson.
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