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GAVI and Ronald Araujo are expected to resolve their contract issues and remain at Barcelona this summer.
Last week it was announced that the duo had rejected three "insufficient" contract offers that had been put on the table.
Spanish outlet Marca reported that the club had started negotiations with incredibly low offers and gradually built up the money each time the proposals were rejected.
No deals have been struck yet, but according to Barcelona president Joan Laporta the negotiations are going well.
When speaking to El Periodico as per , he said: "Gavi and Araujo contracts? There's a framework in which we have to stay at to negotiate salaries. Talks are going well.
"We want them to stay, and they want to stay."
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The news will come as a huge blow to Manchester United and Chelsea.
Both clubs were hoping to sign the pair after their breakthrough season at Barcelona.
The Red Devils are keen to sign Araujo in a bid to strengthen their defence.
Meanwhile, the Blues are also looking for a new centre back to act as a replacement for Cesar Azpilicueta, Antonio Rudiger or Andreas Christensen - all three are set to leave West London in the summer.
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Man Utd and Chelsea have also been linked to Gavi, along with Premier League rivals Liverpool.
However, they will have to act quickly if they don't want to spend an eyewatering sum on the midfielder.
His release clause is set at £42million until June 30, when it will then rise to £100million for the final year of his contract.
Both players' current deals expire in 2023, so Barcelona do not have long to reach an agreement with the pair.