Sport says the 17-year-old's agent with the club expires in the summer of 2023 and he has been linked to a number of top sides over the past season.
Gavi's agent, Ivan de la Pena, is at odds with Barcelona officials over a new contract at the Nou Camp.
De la Pena was unhappy with club president Joan Laporta, for comments he made suggesting Gavi's representatives were dragging out contract negotiations and delaying their decision.
De la Pena instead contests that Gavi is yet to receive a formal renewal proposal from the club.
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