The Croatia international last week stated "my head is already at Liverpool" after claiming that the Merseyside club had a £20 million offer for him rejected.
Liverpool boss Brendan Rodgers is reported to be lining up a fresh bid for the centre-back, who stated that Southampton value him at £25 million, as he attempts to bring in more new faces following the record sale of Luis Suarez to Barcelona.
Southampton manager Koeman has been in contact with Lovren and expects the 25-year-old to join his team-mates on a pre-season trip to Holland and Belgium, amid reports that the former Lyon man could go on strike in order to get his wish to move to Anfield.
"I have spoken to Dejan and I want to keep him. He has a contract. He knows he has to come back." said former Netherlands defender Koeman.
"Liverpool have a lot of money after the transfer of Luis Suarez and they will spend some money.
"I have to do everything to keep the best players but the decision is of the board."
Lovren arrived at St Mary's from Ligue 1 side Lyon just 13 months ago on a four-year deal and made 31 Premier League appearances in his debut season in English football.
Thank you for reading 5 articles this month* Join now for unlimited access
Enjoy your first month for just £1 / $1 / €1
*Read 5 free articles per month without a subscription
Join now for unlimited access
Try first month for just £1 / $1 / €1
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.