A source close to Virgil van Dijk expects him to be a Liverpool player by the end of the window, Sky sources understand.
Liverpool ended their interest in Van Dijk after Southampton complained to the Premier League about an alleged illegal approach.
They also apologised to Southampton.
Liverpool's position has not changed since they issue a statement last month, which read: "Liverpool would like to put on record our regret over recent media speculation regarding Southampton Football Club and player transfers between the two clubs.
"We apologise to the owner, board of directors and fans of Southampton for any misunderstanding regarding Virgil van Dijk. We respect Southampton's position and can confirm we have ended any interest in the player."
We understand Van Dijk still wants to move to Liverpool. He has not gone on a Southampton training camp in France.
There is no suggestion that Liverpool have done anything wrong since they apologised and ended their interest, while Southampton's position remains that Van Dijk is not for sale.
Chelsea and Manchester City are also interested in the player.