This year Lynx UK Trust intends to apply for a licence to trial the reintroduction of lynx to the wild for five years.
It is currently carrying out a stakeholder consultation in the Kielder forest (England) and Borders (Scotland) area.
The NSA says Eurasian lynx are classed as dangerous wild animals under the Dangerous Wild Animals Act 1976, meaning it would be a criminal offence to keep them without a local authority licence.
Currently, these licences are only available for zoo and captive animals.
Phil Stocker, NSA chief executive, said a change in legislation would be needed to make a release legal.
“This is very unlikely to happen in the near future given the raft of priority legislative work needing to be done,” he said.
“Pastoral livestock farming already delivers a highly attractive countryside with environmental, economic and social benefits. I can’t accept that lynx could improve or deliver anything more.”
Current law would allow farmers to legally shoot lynx causing distress to their animals. Lynx UK Trust is working to get this law changed to give protection to released lynx, meaning farmers whose livestock had been killed or injured by lynx could seek compensation from the trust.
NSA opposes this as “it is unlikely that compensation funding could be guaranteed in perpetuity”.
Mr Stocker said: “Even if compensation were offered, it won’t make sheep mortalities acceptable and, given the general public’s reaction to some of the harrowing images caused by domestic dog attacks and their expectation of high animal welfare, I can’t see how distressing attacks caused by a wild animal will be accepted.
“Any licence application to either Scottish Natural Heritage or Natural England will be considered jointly before any decision is made,” he added.
“The species has been absent from the UK for thousands of years, and our countryside now is far too fragmented and built up to support a viable population of lynx. The species would challenge the way our countryside is managed.”