Mundo Deportivo says the 17-year-old has 18 months left on his contract and the Reds are ready to offer him a big wage and hefty signing on bonus.
But Liverpool are also prepared to trigger the youngster's £42million release clause.
They could reportedly offer Gavi a contract worth £3m per year too, as well as a signing on fee of £8m.
That would trump Barcelona's offer, with the Spanish giants still feeling the sting financially.
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