The centre-back joins Rickie Lambert and Adam Lallana at Anfield whilst Luke Shaw has also departed to join Manchester United, and Koeman is now hoping to act quickly to replace Lovren and Shaw.
Vlaar has been continuously linked with a move away from Villa this summer following a solid World Cup campaign with the Netherlands and Koeman is hoping he can convince the centre-back to join Southampton having worked with him at Feyenoord.
Koeman made Vlaar captain whilst in charge of the Eredivisie outfit, and will look to tempt the powerful defender into making the switch by making him captain of the Premier League side if he makes the move.
The 29-year-old has just one year remaining on his current contract at Villa Park and could be an ideal replacement for Lovren.
|Team||Pos||Apps||Goals||Won Tackle / apps||Aerial Won / apps||Interception Won / apps||Total Clearance / apps||Mins|
|Ron Vlaar||Aston Villa||DF||32||0||1.72||1.47||2.00||6.63||2,805|
The Dutchman made more tackles per game than Lovren last season, but the Croatian defender was more dominant in the air and outperformed Vlaar in interceptions and clearances as well.
However, with the new season looming, Southampton must start bringing in replacements for the key players that have left the club this summer and Vlaar would be a good signing nonetheless.
Marcos Rojo would be a fantastic capture if The Saints could secure his services, though he will cost an estimated £17 million.
The left-back, who can also operate in the centre of defence, shone for Argentina at the World Cup and would add quality to the Southampton backline.
He scored four times for Sporting in 25 appearances last season and also grabbed a goal at the World Cup in Argentina's 3-2 win against Nigeria.
The Saints have plenty of money to spend after seeing star players leave for high transfer fees and they should start to reinvest by bringing in some reinforcements.
Would Vlaar and Rojo be good signings for Southampton?