Liverpool are in the hunt for a defensive midfielder this summer following the departures of Fabinho and Jordan Henderson.
The Reds have had several names on their shortlist but Lavia has been one of the priority targets for the Anfield club.
However, negotiations with Southampton have been complicated as the Saints have never moved away from their original asking price of £50m.
Liverpool have had several offers rejected, including the last one of £45m to £46m and according to Belgian journalist Sacha Tavolieri, the Saints expect the Reds to blink.
Southampton believe that Liverpool’s need for a defensive midfielder will force them to match their asking price for Lavia.
The midfielder wants the move and was an unused substitute in Southampton’s win over Sheffield Wednesday last week.
Liverpool have been reluctant to pay such a figure for a 19-year-old midfielder in the ongoing window.
However, the Saints are now confident that the Reds will eventually pay up to get the defensive midfielder their squad need.
