Liverpool coach Brendan Rodgers has already signed Rickie Lambert and Adam Lallana from Southampton in the last two months and is reportedly keen to add the central defender to his list of off-season acquisitions.
"Liverpool sent a £20 million offer and they (Southampton) paid £9 million for me, so they would've earned twice the amount," the Liverpool Echo quoted Lovren as telling Croatian website Sportske Novosti.
"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.
"Liverpool sent the offer and the club haven't informed me. I found out about the bid from other people which disappointed me and I realised I've got no business staying at Southampton."
Lovren, who turned 25 on Saturday, joined Southampton from Lyon in June 2013 and represented his country at the World Cup in Brazil.
- Sports & Recreation
- Liverpool Echo
- Rickie Lambert
- Adam Lallana