Rodri has given Barcelona the go-ahead to begin talks with Manchester City as they try to beat Real Madrid to a deal for the midfielder, a source has told ESPN.
Madrid had been in talks with the player's representatives since last month but, after several days without any progress, Barça had now taken the lead in the race to sign Spain's World Cup-winning captain, the source said.
Another source told ESPN that Rodri's camp believed Madrid had shown the necessary commitment to reach an agreement.
Madrid cannot be entirely ruled out of the race to sign the 2024 Ballon d'Or winner, sources said.
Rodri was keen to return to Spain this summer rather than renewing his contract with City, and the midfielder has been open to the possibility of joining either of the LaLiga giants.
The player is a fan of Barça's style of play, sources said, and has already spoken to coach Hansi Flick, who explained how the midfielder would fit into his vision.
By contrast, Rodri was concerned that Madrid coach José Mourinho had not been entirely convinced about his signing from the beginning, another source said.
Madrid believe Rodri's signing is now complicated, given competition from Barcelona, but the club are willing to make one last effort to get a deal back on track.
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Rodri, 30, underwent minor surgery on a back problem last week, and is currently on holiday after Spain's victory in the World Cup final on July 19.
He excelled at the tournament, picking up the Golden Ball for Best Player, having previously struggled for fitness and form since suffering an ACL injury in September 2024.
A source told ESPN that Barcelona believe there is room in their midfield given the injury suffered by Frenkie de Jong, while Rodri has good relationships with the dressing room at Camp Nou.
Real Madrid have invested heavily in this summer's transfer market, signing Marc Cucurella, Bernardo Silva, Ibrahima Konaté, Denzel Dumfries and Carlos Espí, and announced the signing of Yan Diomande from RB Leipzig on Thursday.
Barcelona have signed Anthony Gordon and Karim Adeyemi, and have been heavily linked with a move for Atletico Madrid's Julián Álvarez.
Information from ESPN's Rodrigo Faez contributed to this story.