“Assessment remains ongoing to ascertain the full extent of the injury and expected prognosis,” City said in a statement.
Reports earlier this week said the 28-year-old Spain midfielder could miss the rest of the season.
Rodri’s loss would be a huge blow to City’s hopes of winning a fifth consecutive Premier League title and ambitions of reclaiming the Champions League.
Manager Pep Guardiola said he had the responsibility to find a way of coping without the midfielder.
“Rodri is irreplaceable,” Guardiola said after City’s 2-1 win over Watford in the League Cup on Tuesday.
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