Marshall, 22, has handed in a transfer request at Celtic and was the subject of a £500,000 bid from City last week. Despite the bid's rejection, the 'keeper remains convinced that Grant's side can match his ambitions.
"Norwich have high hopes of moving up to the highest level so I'd obviously be interested in going back," said the Scot.
"They're one of just a number of clubs in that division who will be going for promotion next season - which makes the Championship one of the most competitive leagues."