The 31-year-old midfielder, who has seen his chances limited under Chris Hughton this term, is anxious to leave and his former boss Paul Lambert is a confirmed fan and appears keen to take him to Villa Park.
Hoolahan asked for a move, but Norwich were quick to turn and released a statement saying: "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."
Hoolahan released his own statement to Sky Sports, reiterating his desire to leave the club.
"Following a meeting with the club chief executive, I felt I had no option but to hand in transfer request, I have noted that request has been turned down - however I believe it is in the best interest of Norwich, for whom I have the greatest respect, and myself that I am allowed to move on and play my football elsewhere."
Hoolahan is under contract until June 2015.