Reports in Spain claim the Reds are willing to offer the 17-year-old a signing bonus close to €10million (£8.5m) five times the €2m Barca have tabled for Gavi to stay.
Rated as their heir to manager Xavi Hernandez' throne as Barcelona's midfield controller, Gavi broke into the senior side this season and quickly followed up with a surprise call-up to Luis Enrique's Spanish national team.
Now a mainstay in Barca's midfield, Gavi scored against Atletico Madrid last time out to help his side rejoin LaLiga's top four.
However, despite a busy January transfer window that saw the likes of Ferran Torres, Pierre-Emerick Aubameyang and Adama Traore arrive at the Camp Nou, Barca may not be able to match offers from the Premier League.
Returning president Joan Laporta announced that the club was in £1.2billion worth of debt on his arrival a year ago, which led to the departure of their greatest ever player, Lionel Messi, on a free transfer to Paris Saint-Germain.
A number of players such as Gerard Pique, Samuel Umtiti and Sergio Busquets have signed new contracts on reduced wages to help the club out of their salary cap crisis.
And now reports out of Catalunya claim Sevilla-born Gavi must 'show his love for the colours' and turn down bigger money on offer in England.
Liverpool have a difficult relationship with Barcelona who have snatched superstars such as Luis Suarez, Philippe Coutinho and Javier Mascherano in recent years, but could get their own back with Gavi.
El Nacional claims the Reds will not negotiate with Barcelona, and instead will head directly to LaLiga's headquarters to trigger Gavi's €50m release clause.