The 42-year-old handed in his resignation earlier this week, which the Canaries rejected, in a bid to replace Alex McLeish who was sacked from Villa Park in May. The Villans then released a statement on Saturday expressing their delight at appointing Lambert as their new manager.
However, Norwich have responded with a statement of their own in which the club have paid tribute to the Scot for his efforts with the side, but insist that no compensation deal has been finalised, contrary to reports.
"The search for the next Norwich City manager is already actively underway and the club has been inundated with applications" - Norwich statement
The official statement says: "Following today's announcement by Aston Villa that they have appointed Paul Lambert as their new manager, we would once again like to place on record our sincere gratitude to Paul for everything he has done for the club - everybody at Carrow Road wishes him all the best for the future.
"Some media reports are suggesting we have agreed compensation for Paul's services with Aston Villa, however this is not the case. We will continue to discuss this matter privately with Aston Villa."
However, the club did reveal they have already begun their search for Lambert's replacement and have received plenty of interest already.
The statement continues: "Meanwhile the search for the next Norwich City manager is already actively underway and the club has been inundated with applications for and interest in the job of leading this great club forward in the Barclays Premier League.
"The next Norwich City manager will have a great squad of players, a robust and competitive budget and excellent facilities to work with - as well as the superb backing home and away of our fantastic supporters.
"The club will update our fans on this process in the days ahead as soon as we have more news."