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."

The US investment bank will switch to video interviews with first-round undergraduate candidates from next month.
Each year the bank hires about 2,500 students as both summer and full-time analysts.
Goldman hoped the move will allow it to find students who do not attend top-tier US universities.
Edith Cooper, Goldman's global head of human capital management said: "We want to hire not just the economics or business undergraduate but there is that pure liberal arts or history major that could be the next Lloyd Blankfein."
Mr Blankfein, the bank's chief executive, went to Rutgers, an institution that is not part of the elite group of US universities known as the Ivy League.
Chief operating officer Gary Cohn went to the American University, also outside the Ivy League.
Goldman recruits from 400 colleges and universities globally and 225 in the US.
The bank will still have a presence on college campuses, but planned to use it promote other opportunities. It will still conduct second-round interviews in person.
The shift will not affect business schools or professional hires, but is part of a broader move by Goldman to use technology in the hiring process.
The new method will include structured interviews, which the bank said will allow for greater comparisons between candidates and "more objective and informed hiring decisions".
Goldman is also experimenting with personality questionnaires, which it feels may help to predict how successful a person will be at the firm.
Farmers and landowners have been asked for their views on a proposal to bring back lynx to parts of Scotland and England.
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Goldman Sachs is scrapping face-to-face interviews on university campuses in a bid to attract a wider range of talent.