The Reds lodged a final ‘take it or leave it’ £25m offer for the England international on Friday, but their bid is understood to have been dismissed by the Saints.
Yet now the 26-year-old has told the club’s board that he wants to move on, but he has stopped short of submitting an official transfer request for the time being.
However, it is thought that the South Coast club are willing to play hardball to keep their man or force Liverpool to offer £30m.
Southampton are keen to entice more cash from last season’s Premier League runners-up, with 25% of any fee set to go to Bournemouth as a part of the deal that saw him move between the clubs as a youngster.
The Hampshire side have also released a statement stating that they will not sell star names until the identity of their new manager is known, which further complicates the situation.
However if Lallana submits an official transfer request they may be powerless to resist.
It remains unclear as to whether or not the playmaker will be willing to go to such lengths due to his love of the club.
If the move does go through, he will join Rickie Lambert at Anfield.