Manchester City have confirmed that Rodri is set for a period on the sidelines after undergoing back surgery.
The midfielder underwent the procedure on Monday after "feeling discomfort for some time."
City are hopeful the 30-year-old, who has been heavily linked with a summer move to Real Madrid, will only require a "short" recovery period.
A statement issued by City on Tuesday read: "Manchester City can confirm Rodri has undergone successful minor back surgery.
"The midfielder had been feeling discomfort for some time but has now undergone a procedure to address the issue and will now begin a short period of rehabilitation."
Sources have told ESPN that City have not given up hope of agreeing a new contract with Rodri, who has one year remaining on his deal.
However, the club are braced for a bid from Real Madrid after his performances for Spain at the World Cup.
City have already bolstered their midfield with the signing of Elliot Anderson from Nottingham Forest.
There is also interest in Lille's Moroccan midfielder Ayyoub Bouaddi.