Rodgers identified Van Dijk as a potentially excellent addition for his side during his time at Anfield.
However, Liverpool’s scouts told him that Van Dijk was not right, and he ended up having to look elsewhere.
“Virgil van Dijk could have jumped from Celtic to a Liverpool,” Rodgers said. “Some clubs will want to see the players tested at certain arenas first.
“There is maybe an issue with scouts.
“When I was at Liverpool I asked about van Dijk and he was at Groningen and then at Celtic. But I was told he wouldn’t be for us at the time.”
Van Dijk ended up leaving Celtic to join Southampton, and Liverpool’s decision to overlook him could prove costly.
Van Dijk has gone on to become one of the Premier League’s stand out centre-backs, and he is now worth a huge amount of money.
Southampton face a fight to keep hold of the Dutch international, with Liverpool now believed to be interested in signing him.
If Van Dijk does leave Southampton, Celtic will receive a percentage of any transfer deal, which could be a good earner for the Glasgow club.