Keeping elephants in zoos or safari parks could be banned, reports suggest.
Under legislation there would be a ban on importation of any new animals and the existing population will be allowed to die out naturally.
The Mail reported the move was being considered.
Campaigners have warned the highly intelligent animals suffer from mental illness in zoos.
Research by the RSPCA found elephants in captivity lives for just an average of 17 years and can suffer from illnesses, including arthritis.
In the wild they can live for between 50 and 70 years.
The first elephant arrived to Britain in 1255 under King Henry III.
There are thought to be about 50 elephants in captivity at zoos across the UK including at Colchester.
Other zoos include Woburn, Whipsnade, and Chester.
A senior source told the Mail: "Once the current load of elephants die out we will say you can't replace them.
"It's impossible to keep them in conditions where they are happy, the space is too small.
"In the UK the biggest elephant enclosures are so minute.
"They grub up the environment so quickly too – they have an incredibly important role in that but if they are in such a small area they destroy everything.
"It's very likely we are going to say you can't make elephants happy in zoos, we should instead be focusing on elephant conservation in areas that have elephants."
Will Travers OBE, from charity Born Free which has campaigned on the issue for years, said: “The complex needs of this exceptionally intelligent, sensitive and social species can never be met in a zoo – captive elephants can suffer physically and psychologically.
"Ending their exploitation is why our work began nearly 40 years ago, so this news is deeply poignant and significant for our charity.”
But it is understood there are no plans to impose a ban at the current time.
Instead the Government is expected to repond to a report in regards to the issue next year.
Dr Jo Judge, CEO of the British and Irish Association of Zoos and Aquariums, said: “We were delighted to meet with Minister Lord Goldsmith who confirmed that Defra have no intentions to ban elephants. And we are pleased that Defra will support an evidence-based approach to caring for elephants in the UK.
"I’m proud that zoos continue to work closely on reports that inform Government decisions regarding elephants, which have shown many welfare improvements over the years to the point where BIAZA zoos lead the world in elephant care.”
“BIAZA zoos not only provide loving homes for these complex and intelligent animals but they are at the heart of much of the conservation work carried out by good zoos. Whether that is testing of conservation equipment (such as thermal imaging or camera traps) that allow us to protect wild families of elephants, pioneering vaccines against diseases or converting spend from a family day out into conservation funds that protects many other species.”
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