The Spanish left-back was thought to be on the verge of joining the Reds last week, however negotiations between the two clubs have hit a brick wall.
It is understood that Liverpool value the youngster at around £13.5m, which is some way short of Sevilla’s asking price.
A five-year contract has been agreed in principle with the player, but as it stands, a deal will not go ahead.
As a result Brendan Rodgers is already eyeing up alternatives, with Rojo in the frame.
The Sporting Lisbon full-back has been linked with the Merseysiders for some time, but it is thought that he fine display in Argentina’s World Cup opener against Bosnia has seen interest from the Premier League giants intensify.
Rojo is seen as a more cost-effective option, with an offer of around £10m likely to be successful with the Portuguese club having indicated that they will sell for the right price.