Barca will make "a big financial effort," one club source said, to come to an agreement with Gavi's agent, former midfielder Ivan de la Pena. They have drawn up a contract that will run until 2027 and include a €1 billion release clause.
The two parties are looking for a date to sit down and close the issue once and for all. Sources on both sides of the talks are optimistic an extension will be agreed soon, with the player's deal due to expire in summer 2023.
Gavi, 17, has had a breakout season for club and country, but Spain coach Luis Enrique suggested last week that "he remains unknown even to those close to him" in what was taken to be a dig at Barca as they dragged their heels during contract negotiations.
Luis Enrique denied it was intended for the Catalan club, though, saying he was "talking in general," just days before Gavi became Spain's youngest ever scorer, breaking Barca teammate Ansu Fati's record.
Talks to renew Gavi hit a stumbling block two weeks ago when Barca president Joan Laporta said he did not understand why De la Pena was considering other offers when he had a good proposal from the Blaugrana on the table.
Sources close to Gavi's camp told ESPN at the time that they were still waiting for Barca's official offer.
However, that friction has been overcome, with Barca viewing Gavi as one of the pillars of the club's future on the pitch moving forward, along with Pedri, Ansu Fati and Ronald Araujo, who have all signed long-term deals recently.
Barca's bet on Gavi is also, in part, linked to the club's financial situation, with sources acknowledging losing him would be a hammer blow given the lack of resources to replace him.
The Catalan club hope members will next week authorise them to sell a stake in future merchandising and television rights, which would give them some room to breathe.
Sources have previously told ESPN the sales could bring in as much as €700 million, with vice president for finance Eduard Romeu telling Diario Sport on Thursday Barca "need €500m" to save themselves.