The Southampton centre-half was Jurgen Klopp's number one transfer target this summer with the club confident of beating Manchester City and Chelsea to his £60million signature.
But following initial discussions between the two parties and reports that the Dutchman had agreed to move to Anfield the Saints reported the Reds to the Premier League.
Southampton's grievance prompted an immediate apology from Liverpool - accepted by the south-coast side - and a commitment to end their interest in the 25-year-old.
A preliminary investigation was launched by the Premier League but has stalled as there is insufficient evidence to support Southampton's claim.
It is understood unless new information comes to light there will not be any more progress with the inquiry, effectively allowing Liverpool to avoid a sanction.
Liverpool are expected to be busy in the market this summer as Klopp looks to build a squad capable of challenging both at home and abroad after securing Champions League football on the final day of the season.
Mohamed Salah has already signed from Roma in a £34.3m deal while Dominic Solanke will join when his Chelsea contract expires at the end of the month with the fee to be decided by tribunal.
Klopp is keen to get at least seven new faces through the door but faces a fight to secure Naby Keita with RB Leipzig holding out for £70m for the Guinea international midfielder.
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