Liverpool want to make Lovren their third signing from Southampton this summer, following moves for Adam Lallana and Rickie Lambert, and have already failed with a £20m bid.
The centre-half says his "head his already at Liverpool" and, at his first official press conference since succeeding Mauricio Pochettino, Koeman offered no guarantees Lovren will start the season at St Mary's.
But the new manager struck a defiant note despite the high-profile summer departures and expects to add Feyenoord striker Graziano Pelle to recent signing Dusan Tadic in the coming days.
He said: "We'd like to keep the rest of the good players and bring new players in, but this is the situation in football with all the clubs and all the teams - look at Luis Suarez going to Barcelona
"There's a lot of movement with players, but we'll continue with the philosophy of Southampton Football Club: that means we like to bring in young players; that means we'd like to continue from the fantastic season last season. We still we have that ambition to go forward."
Koeman criticised Lovren for going public with his wish to leave but said he expected the Croatia defender to report for training on Sunday.
Pressed on Lovren's future he said: "Of course you'd like to have all the players in the squad happy to be at Southampton.
"If there is a different opinion we will speak about it and finally the board has to make a decision. I hope he will come back.
"The last time I spoke to him was four or five days ago. He said it's a difficult situation and he will have another talk to the club and his agent, but he knows he's still a Southampton player and has to come back."
Serbia midfielder Tadic joined from FC Twente last week as a direct replacement for Lallana, and a deal for centre-forward Pelle is now imminent.
Koeman said: "Pelle is close but it's still not signed. We're getting closer together and we hope maybe this weekend to have him as the second new signing.
"Tadic is a player who scores and makes assists. I know him very well from holland an it's a player who has very similar qualities to Lallana. He's a great player for us."