Manchester City confirmed on Wednesday that Rodri suffered ligament damage to his right knee during their 2-2 draw with Arsenal, although the full extent of the injury remains unclear.
The midfielder has been in Spain this week consulting specialists after limping off during the first half of the match at the Etihad Stadium on Sunday.
"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.
"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."
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.