The 22-year-old has been the subject of growing speculation ahead of the winter transfer window, with his reduced involvement under Hansi Flick prompting suggestions that he could consider a fresh start elsewhere.
Bayern Munich and several Premier League clubs have previously been linked with the midfielder, while Napoli have emerged as the latest reported suitor.
However, claims that the Italian club have explored a potential deal have been firmly rejected by De la Peña, who insists there have been no discussions with interested parties.
"I have not negotiated with anyone. Gavi is staying," the agent said, delivering a clear response to the growing speculation.
The message reflects the player's own position. Gavi remains determined to establish himself at Barcelona and has no desire to abandon his ambition of becoming a leading figure at the club where he developed.
Having overcome a difficult period with injuries, the midfielder believes he needs a sustained run of appearances to demonstrate what he can offer Flick's team.
He is not understood to be considering offers from other major European clubs, despite the uncertainty surrounding his current role.
Gavi has found opportunities harder to come by in a competitive Barcelona midfield, with Flick having several established options available. The arrival of Rodri has added further competition, while Pedri and other midfielders remain important figures in the German coach's plans.
Nevertheless, Gavi is convinced that continuity and regular minutes will allow him to rediscover his best form. He does not regard a move elsewhere as the answer to his current situation.
De la Peña's intervention is also intended to put an end to suggestions that he has been sounding out clubs or negotiating potential terms ahead of January.
For now, the position from the player's camp is unequivocal: Gavi wants to remain at Barcelona and fight for his place rather than look for an exit.