The London Evening Standard says the Reds are planning to take up an option on Lovren's contract that will tie him to the club until 2022.
The Croatian, who has slipped down the pecking order at Anfield in recent seasons, is attracting interest from across Europe ahead of a potential summer move.
Zenit Saint-Petersburg became the latest club to join the race for his signature, and were given encouragement that they could strike a deal with the Reds.
However, hopes of a cut-price move appear to have been dented after it emerged that Lovren's contract will not have just one year remaining this summer.
That is because the Premier League champions plan on triggering a one-year option at the end of the transfer window.