The Premier League is waiting on further information from both Southampton and Liverpool over an alleged illegal approach for Saints defender Virgil van Dijk before deciding whether an investigation would be appropriate, Press Association Sport understands. The Reds have now "withdrawn their interest" in the Dutchman, who was believed to have been Jurgen Klopp's top summer transfer target and had apparently indicated his eagerness to become the latest player to swap St Mary's Stadium for Anfield. Liverpool also issued an apology to Southampton on Wednesday evening for "any misunderstanding regarding Virgil van Dijk". Press Association Sport understands the Saints had asked the Premier League on Tuesday to investigate an alleged illegal approach, which led to high-level talks on Wednesday and was followed by Liverpool's statement expressing " our regret over recent media speculation regarding Southampton and player transfers between the two clubs." It is not expected the Premier League will receive the additional information requested until Monday, but if it is determined both clubs now believe the matter to be closed, a full-blown investigation appears unlikely . Although Van Dijk's proposed Â£60million switch to Liverpool - where the defender was reportedly set to become the highest-paid player at Anfield - may seem off the agenda, uncertainty over his long-term future at Southampton could well rumble on. Both Chelsea and Manchester City have been touted as being interested in acquiring his services as well as leading clubs in Europe. Van Dijk, meanwhile, issued a cryptic post on his personal social media accounts during Thursday afternoon. The 25-year-old was pictured aboard what looked to be a private jet and staring out of the window with a single 'thought balloon' Emoji. The Holland international joined Southampton from Scottish champions Celtic in September 2015 and last year penned a new deal which committed him to the south-coast club until the summer of 2022. Southampton insist they will no longer be bullied in the transfer market, having seen the likes of Adam Lallana, Nathaniel Clyne and Dejan Lovren all leave for Liverpool in recent seasons, while Luke Shaw and Morgan Schneiderlin joined Manchester United, and captain Jose Fonte headed to West Ham in January. Chairman Ralph Krueger told Press Association Sport: "We do not need to sell any player for the first time since I have been here. "I can make that statement and - unless football decides it is in the best interests - we don't need to do that."