Arsenal Football Newsletter
The midfielder suffered a groin injury in the crucial win over Arsenal on Sunday, playing 88 minutes before he was replaced in the closing stages.
Rodri underwent tests to determine the severity of that issue, and Pep Guardiola confirmed at his pre-match press conference that the Spaniard will not be available to face Burnley.
"I think for tomorrow he will not be ready," Guardiola said on Tuesday.
Rodri also remains a doubt for the FA Cup semi-final clash with Southampton at Wembley this weekend, but City do have a significant gap before they then resume their Premier League campaign.
"We'll see in the next games, semi-final against Southampton or in 12, 13 days against Everton," Guardiola said.
In his absence, Nico Gonzalez could come into the side, and Guardiola backed him to step up.
"Nico Gonzalez has helped us a lot, a lot this season in the absence of Rodri, and he's helped us to be in the position that we are right now," the City boss said.
City will be desperately hoping to have Rodri available for the final weeks of the season as they target a domestic treble.
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They will be confident of beating Burnley even with the midfielder on the sidelines. Victory at Turf Moor would move them to the top of the Premier League table.
City have more than a week off between their FA Cup semi-final and a trip to face Everton in the league on May 4, providing Rodri with a gap to potentially recover.
The 2024 Ballon d'Or winner missed a significant chunk of the first half of the season with a hamstring injury.
He has struggled for consistency since returning from an ACL injury at the end of last season, but has been back closer to his best form in recent weeks.
City will also be without Ruben Dias against Burnley, with the defender yet to recover from an ankle injury.