The 17-year-old has established himself in Xavi's starting 11, featuring 23 times in La Liga and the Champions League group stages this season, his first full campaign as a senior pro.
Gavi signed a contract with the Catalan giants in the summer running through to 2023, but within the deal there is a €50m (£41.7m) release clause which is not out of reach for many other top European clubs.
However, according to El Nacional, the young Spanish international will not be lured to higher wages at Manchester City or a Premier League move to play at Anfield.
Xavi is believed to be a major reason behind Gavi's desire to remain at Barca, with his now manager being an idol of his childhood and the report also suggests that Gavi would find it difficult to transition to England due to language barriers.
During his 17 La Liga appearances so far this campaign, Gavi has netted once and provided three assists for Barcelona.