Sky Sports report says, Southampton asked the Premier League to probe the Anfield club over an alleged illegal approach for the Southampton defender after reports said the player had told Jurgen Klopp he wanted to join the Reds.
Liverpool later ended their interest in signing Van Dijk and issued an apology to Southampton.
However, a preliminary probe by the Premier League has failed to find sufficient evidence to support Southampton's claim.
Liverpool will therefore avoid any punishment unless any new information is forthcoming.
The Premier League has strict rules governing transfers, which means clubs can only negotiate with players once a transfer fee has been agreed with the selling club or if the player is out of contract.
Approaches via an intermediary are also out of bounds.
Van Dijk joined the Saints from Celtic for £13m in September 2015 and signed a new six-year contract last year. Southampton have repeatedly said they have no intention of selling him.