With his deal having a year to run, Gavi has attracted interest from the Reds.
However, Sport says Liverpool have pulled back in the last 24 hours after learning from agent Ivan de la Pena that Gavi's priority is to stay at the Nou Camp.
There remains a big difference between the two parties over new contract talks, but Gavi is still eager to stick with Barca.
Barca's latest offer runs to 2027 and is a major improvement on his current €100,000 salary.
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