Hoolahan has been strongly linked with Villa, who are managed by former Norwich boss Paul Lambert.
The Republic of Ireland international has made just five Premier League starts for Norwich this season, but the Carrow Road club appear determined not to sanction a sale.
A statement on Norwich's official website read: "City can confirm Irish international midfielder Wes Hoolahan has today submitted a transfer request which has been rejected.
"The board of Norwich City has stated clearly no senior players will be sold against the club's wishes and Hoolahan, 31, is contracted to the club until June 2015.
"The club will make no further comment at this time."