The Lynx UK Trust has suggested trial reintroductions in Aberdeenshire, Argyll, Northumberland, Cumbria and Norfolk.
It said the plan has public support and research it commissioned sets out benefits of the big cats' return.
The National Farmers Union (NFU) has previously raised concerns.
Scottish Natural Heritage, which is funded by the Scottish government, has also said reintroductions were "complex" and needed "considerable planning" to meet UK and international guidelines.
Lynx became extinct in the UK 1,300 years ago.
The Lynx UK Trust said 91% of 9,000 respondents to a survey it carried out were in favour of lynx being brought back to help control deer numbers.
AECOM, consultants the trust commissioned to examine the benefits of lynx, have suggested that the cats could benefit eco-tourism as well as prevent deer from damaging crops.
The trust said it now wants to hear views from landowners and farmers.
Dr Paul O'Donoghue, of the trust, said: "Lynx reintroduction is a big step for all of us in the UK and this is the opportunity for a wide range of groups to really understand what it could mean, how they could be affected, and to tell us and the statutory agencies how they feel about it."
Other organisations, including the Scottish Wildlife Trust, Trees for Life and Rewilding Britain, have separately said lynx could form an important part in "rewilding" areas of the UK.
The Cairngorms National Park Authority has in the past weighed up the pros and cons of bringing back the big cats, and also wolves and bears.
Of the three predators, lynx were deemed to have the least negative impact on farmers' businesses.
NFU countryside adviser Claire Robinson said reintroductions raised "big concerns" for farmers in England.
She said: "Any species introduction, particularly if it has not been in this country for hundreds of years, can have a massive impact on the many benefits that the countryside delivers.
"The environment has changed drastically and we do not know how lynx would behave in the current environment.
"But the biggest concern we have would be the impact on farm animals with lynx preying on lambs, poultry and outdoor piglets - those animals are farmers' livelihoods."
Farmers and landowners have been asked for their views on a proposal to bring back lynx to parts of Scotland and England.