The Villans confirmed on their official website earlier today that the Scottish boss had agreed to become their new manager on what is believed to be a three-year deal.
However, the Canaries have confirmed that no financial agreement has been reached for Lambert to make the switch to Villa Park.
"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," read a statement on the club's on the official website.
"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."
Lambert had been in charge at Carrow Road since 2009.