According to the Daily Mail the centre-back gave notice of his desire to move on from Southampton after only joining last summer via an email sent out to executive director Les Reed and chairman Ralph Krueger on May 30.
The email is beileved to have outlined Lovren's wish to move this summer in order to fulfill his ambition of playing Champions Legaue football next season.
As yet the Southampton board have not acknowledged receipt of such correspondence and will be loath to lose another player after Rickie Lambert's Liverpool move to add to the possible departures of Luke Shaw and Adam Lallana to Manchester United and the Reds respectively.
The 24-year-old is also thought to have become unsettled by the recent managerial upheaval following Mauricio Pochettino becoming the new Tottenham boss and with Southampton yet to appoint his replacement.
Lovren discussed his future at the end of the season with the Saints hierarchy when it became known Liverpool were interested in his services. The email was shortly sent out following that meeting.
Despite having an outstanding season the Croatia international is somewhat of a risk should he end up with the five-time European Cup winners.
Whether he is an upgrade on either Mamadou Sakho or Martin Skrtel is questionable yet Liverpool manager Brendan Rodgers has probably been persuaded by Lovren's leadership qualities.
His versatility in that he can play as either the left or right centre-back is something that none of Agger, Sakho, Toure or Skrtel can do and perhaps makes him the leading transfer target for the position.
Roma's Mehdi Benatia would be a better bet but his £30 million price tag coupled with his 27 years of age would make him a non-starter for Liverpool owners FSG.