The pitch at the Sky Blues' new Ricoh ground will not be ready in time for the opening day game on 6th August.
"As the Ricoh Arena will not be able to stage a fixture until 20 August, we will liaise to see if it's possible," said a Coventry spokesman.
"If Norwich are unable to facilitate this request, we will find an alternative stadium in which to play.
"Several venues have been deemed appropriate and the Sky Blues will look at every option in order to minimise disruption for our supporters."