The Association said the move highlighted Mr Paterson's undoubted commitment to eradicating England of bovine TB.
CLA President Harry Cotterell said: "It is absolutely right that Mr Paterson is considering extending the pilot badger cull in Gloucestershire, which has proved to be safe and humane.
"This area was always a testing ground to establish an effective method of ridding England of the devastating effects of bTB and it is clear we need to allow more than six weeks to achieve the best results.
"While the cull has been challenging, and progress was initially slow, extending the cull is crucial if we are going to see an impact on the disease."
The Association said the pilot culls were just the first step in a 25-year action plan to rid England of a disease which led to 38,000 cattle being slaughtered in Britain in 2012.
Mr Cotterell added: "The appalling effects of this disease cannot simply be ignored. Government and farming must continue to work together if we are to win the fight against bTB."