Manchester City manager Enzo Maresca has admitted "anything can happen" regarding Rodri's future amid reports Barcelona have made a bid for the Spain midfielder.
City are understood to have rejected an opening offer of £38.5 million ($52 million) from the LaLiga champions, with the Premier League club reportedly valuing Rodri at around £68 million.
The 30-year-old has just one year remaining on his Manchester City contract and has been strongly linked with a return to his native Spain.
Rodri was named Player of the Tournament at the recent World Cup in North America, where he played a starring role in Spain's triumph.
Barcelona could return with an improved offer, while Rodri's potential departure could prompt City to pursue Chelsea midfielder Enzo Fernandez.
Rodri was the final City player to return for pre-season, reporting back on Friday after undergoing back surgery following the World Cup.
Speaking ahead of City's Community Shield clash with Arsenal, Maresca refused to rule out further transfer activity.
"First of all, we already said the transfer window is open, we can buy and sell players, anything can happen," Maresca said on Friday.
"I just saw Rodri now in the building, I gave him a big hug. He looks good, so we'll see what happens."
Maresca declined to discuss players contracted to other clubs but acknowledged that Manchester City still have business to complete before the summer transfer window closes.
"For sure there are things we need to do," he said. "Now, how many, I don't know. It can be one, can be two, it depends also if players are going to leave."
Rodri joined Manchester City from Atletico Madrid in 2019 and became a key figure under former manager Pep Guardiola.
The midfielder helped City win multiple Premier League titles and played a crucial role in their 2023 Champions League triumph.
His success continued internationally as he won Euro 2024 with Spain before claiming the 2024 Ballon d'Or.
However, a serious knee injury subsequently kept him sidelined for much of the 2024-25 season.
Chelsea have reportedly set a Friday deadline regarding an offer for Argentina midfielder Enzo Fernandez.
Asked whether City could submit a bid before that deadline, Maresca played down the prospect of an immediate move.
"Not today to be honest, I don't think we're going to do something today," he said.
City have already spent £116 million on England midfielder Elliot Anderson following Bernardo Silva's departure, but another midfielder could soon leave the Etihad.
Tijjani Reijnders is reportedly close to joining Saudi club Al Qadsiah in a deal worth an estimated £51 million.
Reijnders joined City from AC Milan for £46.5 million last year but started only half of the club's Premier League matches.
Maresca said it was understandable for players to seek moves when they want more regular playing time.
"Tijjani's situation is like James Trafford's situation, some more players, but I think when the club, the player, the manager, they all think the same way, that probably the best decision for a player is to go, you have to go."
Manchester City's immediate focus turns to the Community Shield, where FA Cup holders City face reigning Premier League champions Arsenal.
Mikel Arteta's side finished seven points ahead of second-placed City last season as Arsenal ended their 22-year wait for a Premier League title.
Maresca acknowledged Arsenal's strength but insisted City are determined to close the gap this season.
"Arsenal have shown in the last two or three or four, five years, that they are always there," Maresca said. "It is a fantastic team from Mikel.
"They won the Premier League, they showed how good they are in this moment. But at the same time, we are City and we're going to try to close the gap and compete."
