The big cats became extinct in the UK 1,300 years ago.
Lynx UK Trust, a charity, wants to reintroduce the animals to selected locations in the UK and has requested a meeting with SNH.
In a statement, SNH said reintroductions were "complex" and needed "considerable planning" to meet UK and international guidelines.
An area near Huntly in Aberdeenshire has been indentified as a potential location for releasing Eurasian lynx.
SNH has been involved in the reintroduction of sea eagles and rare woolly willows and also a trial release of European beavers.
Its statement said: "If we received an application to reintroduce lynx, we would be looking for the applicant to provide information on how the project would address ecological issues such as habitat availability, as well as the views of the public, livestock and land managers, the wider UK perspective, and any socio-economic impacts.
"The views of the Scottish government would need to be taken into consideration. A significant amount of evidence is required to support an application."
It added: "The Lynx Trust have requested a meeting with SNH to discuss how these conditions might be met."
Last October, other conservationists argued that efforts to "rewild" parts of Scotland should involve the reintroduction of lynx.
Alan Watson Featherstone, of Trees for Life, said the predator could "play a crucial top-down regulatory role in ecosystems" by helping to control red and roe deer numbers.
Scottish Natural Heritage (SNH) has set out its position on the possible reintroduction of lynx to Scotland.