The Croatian centre-back is a rumoured target for the Reds, who are understood to have had an initial £20m offer for his signature turned down by the Saints.
Lovren himself was angered by the backtracking from his club, who he believed to have agreed to sell him if such a sum was offered.
The defender said in the aftermath of the incident that he already considered himself to be “at Liverpool”, and that it would be tough for him to return to post-World Cup training with Southampton.
However, the 25-year-old has indeed linked up with the squad after being slammed by new manager Ronald Koeman for his behaviour.
Yet, it is understood that he still wants to force through a switch to Anfield before the new season starts.
Lovren would become the third player to swap St Mary’s for Merseyside this summer, following Adam Lallana and Rickie Lambert to the North West.
Jay Rodriguez may also make the move, with reports claiming he’s the latest Liverpool target.