Foden has 24 goals for City in all competitions this season and has often been utilised in more central roles by coach Pep Guardiola
Real did not immediately respond to a request for comment on the report.
The story in ABC said Zidane learned of the contact testing positive on Thursday morning and subsequently did not attend Real Madrid's training session ahead of Saturday's La Liga game away to Osasuna.
The report added that the Frenchman had undergone a COVID-19 test and is awaiting the result, although La Liga must approve his return to work as its protocols dictate that a person should isolate for three days and then get a negative test before returning to training or take part in a match.