The Reds are believed to have made an offer for the centre-back earlier this summer, which was rejected by Southampton, who had already seen boss Mauricio Pochettino, Rickie Lambert, Luke Shaw and Adam Lallana depart.
Lovren is believed to want to move to Anfield, and Koemen is reportedly lining up Aston Villa and Netherlands defender Ron Vlaar as a replacement if the Croatian does move on.
Speaking after Southampton’s 1-0 pre-season friendly victory over Swindon on Monday night, Koeman insisted they have had no formal contact from Liverpool in the past week over a possible deal for Lovren.
Asked if there had been a new bid, he told Sky Sports News: “We have had no bid from Liverpool for Lovren, that is the situation.
“If that does not change, he will continue to play at Southampton.
“We know there is a lot of interest in our players, I think that is normal. But we have to wait, we work on the team.”
Koeman managed Vlaar during their time in the Eredivisie with Feyenoord but refused to be drawn on whether he will move to sign the Netherlands international.
“I know him (Vlaar) from when he was playing at Feyenoord,” added Koeman.
“It depends on the (Lovren) situation but we will decide who we bring in. There are a lot of rumours in football and I can do nothing about that.”
Koeman also revealed that striker Dani Osvaldo, who spent the second half of last season on loan at Juventus following a training ground altercation with Jose Fonte, has been given permission to report back late for pre-season training - though his days at St Mary's look to have come to an end, with the club looking to sell.
“He was late, he had a talk with the board and we decided he can stay away,” said Koeman. "We have to look for opportunities for him to play in a different team."