The article said scientists would only be allowed to use cloning techniques for research initially, but eventually, cells taken from embryos could be used to grow new organs or tissue including brain cells and skin.
Ministers have been considering a report from the government's chief medical officer on whether to allow limited research into human cloning.
The article was sparked by Lord Sainsbury's comments that he thought, on balance, the benefits of allowing research outweighed the downside.
But he said on Sunday the remarks were his personal views, not those of the government.
Ethical concerns
The government is due to release its decision on the controversial issue in September.
The Observer suggested ministers had already decided to allow cloning under strict guidelines.
The article said scientists would only be allowed to use cloning techniques for research initially, but eventually, cells taken from embryos could be used to grow new organs or tissue including brain cells and skin.
Ruth Deech, chairman of the Human Fertilisation and Embryology Authority, said approval of human embryo cloning "must be on the minds" of the government.
She told BBC Radio 4's World This Weekend that nobody wanted the cloning of babies, but there was a growing consensus that good could come out of "therapeutic cloning" of embryos.
"The research would be looking for ways to grow new cells and tissues to help people with Parkinson's, with Huntington's, with Alzheimer's, with cancer and with burns."
She added: "It will be gradual and every step will be checked by us. We give licences and we can take them away."
Religious groups and "pro-family" organisations are among those who regularly raise concerns about the ethics of cloning tissue from embryos.
"We are fundamentally opposed to any such development" said Tom Horwood, spokesman for the Catholic Church.
"A human embryo is a human life. It is creating a human life for the purposes of cloning."
'Tissue bank'
In May this year, the government received a report from the Chief Medical Officer Professor Liam Donaldson.
Prof Donaldson and an expert group of scientists and geneticists were asked to look into proposals to carry out research on cells which have been removed from a young embryo.
Cloning could lead to people having a 'tissue bank' which could be used to help them overcome illnesses such as diabetes or lung disease.
A Department of Health spokesman said: "If someone has damaged tissue in their liver, you may be able to develop some cells into new liver tissue which you could transplant to replace the damaged tissue.
"The government will be publishing the report and its response in two weeks' time. Obviously that is when we will make the government's view known."