The Croatia international is reportedly keen to link up with former team-mates Rickie Lambert and Adam Lallana, who have both left St Mary's for Anfield this summer.
But Southampton are refusing to do business and are holding out for a £25m fee for a player who joined them for £8.5m from Lyon last June.
The 24-year-old, who is currently on holiday following Croatia’s World Cup elimination, scored in Southampton's 1-0 win at Anfield last September.
Liverpool have spent around £35m this summer on Lambert, Lallana and Emre Can, while negotiations are continuing with Barcelona over a possible deal for Luis Suarez.
At this point, buying the whole club for £175 million would probably have been a cheaper option- lee