The Croatia international, who played for Niko Kovac's team at the World Cup in Brazil, has been strongly linked with a move to Anfield.
And the Press Association (h/t The Guardian) reported on Friday that an offer of less than £20 million by Liverpool for Lovren had been rejected by Southampton.
However, in an interview with Croatian website Sportske Novosti, the defender admits to being frustrated at the situation.
Lovren is quoted in the Liverpool Echo article as saying:
Liverpool sent a £20 million offer and they (Southampton) paid £9 million for me, so they would've earned twice the amount.
At this point, I don't know what I'll do and I don't like it.
It was unbelievable that a few days ago I had an offer of £20 million. It was in the morning and by the afternoon the club had said I was not for sale.
Frankly, my head is already at Liverpool.
And Lovren claimed he has been unimpressed with the lack of communication from his current employers, according to the article:
Liverpool sent the offer and the club haven't informed me.
Not even about the subsequent Liverpool bids. That wasn't right.
I found out about the bid from other people which disappointed me and I realised I've got no business staying at Southampton.
However, Lovren also cited the sales of leading Southampton stars such as Rickie Lambert, Adam Lallana and Luke Shaw already this summer as a reason for wanting to leave St Mary's Stadium.
The 25-year-old, who joined the Saints from Lyon in June 2013, also believes the loss of head coach Mauricio Pochettino underlines a lack of ambition at the club.
Lovren is quoted as saying:
I'd gladly stay in Southampton if the club had any ambitions, if they kept the key players, not even the Liverpool bid would have dissuaded me.
When I decided to go to Southampton, many people were surprised, but I went because the people at the club had great ambition.
They gave me assurances about the project—the former chairman, Nicola Cortese, and the former coach, Mauricio Pochettino, convinced me. They gave me incredible confidence.
When the chairman left, and Pochettino was going too as early as April, I realised things had fallen apart.
Liverpool is one of the biggest clubs in the world. Only Real Madrid have as many fans around the world. The last time I played at Anfield, I got chills when I heard 'You'll Never Walk Alone.' I would like to listen to it all the time.
However, one man who has been unimpressed with Lovren voicing his desire to leave Southampton publicly is Saints legend Matt Le Tissier.
The former England international, who remained with the Saints throughout his career, used his official Twitter feed to dismiss the defender's claims.
This transfer tale still has some way to run.