Recent reports have suggested that the 28-year-old Spain midfielder may be out for 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.
"When a team doesn't play with the best midfielder in the world for a long, long time of course it is a big blow but my duty is to find a solution so that we remain competitive as we have been for many years.
"When one player is irreplaceable you have to do it as a team and this is going to happen."
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Rodri has been touted as a potential Ballon d'Or winner after his influential role in City's latest Premier League triumph and Spain's success at Euro 2024.
(This story has not been edited by staff and is auto-generated from a syndicated feed.)