Earlier this month, Liverpool issued a statement on their website apologising to Southampton "for any misunderstanding" amid tapping-up allegations after it emerged the player was keen on a move to Anfield.

Southampton had asked the Premier League to investigate an alleged illegal approach from Liverpool for Van Dijk, having received no contact from the Merseyside club.

Prior to the allegations being lodged, sources told ESPN FC that Van Dijk indicated to Liverpool that they were his preferred destination in the summer ahead of Chelsea and Manchester City.

Sources say the Premier League are unlikely to take any further action due to no new information being provided.

Liverpool's statement on June 7 also added that the club had ended any interest in the Southampton centre-back.

Van Dijk signed a six-year contract last May, and Southampton chairman Ralph Krueger recently said the club could realistically turn down a £60 million bid for the Netherlands international.

"Can we? Yes," Krueger said. "We do not need to sell any player for the first time since I've been here."

In April, Liverpool were given a two-year academy transfer ban, with the second year suspended, for "tapping up" a Stoke City youngster.