Lord Saatchi has been promoting his plan for some years following the death of his wife from ovarian cancer.
He wants doctors to be given new legal protections for testing new treatments on patients.
But he has been opposed by medical insurers and the British Medical Association.
According to the Daily Telegraph, Lord Saatchi has agreed amendments to win backing from health secretary Jeremy Hunt.
The newspaper claims the General Medical Council may also give support to the new proposals.
The latest changes would require a doctor planning to use the provisions of the Bill to seek advice from a specialist colleague first.
Lord Saatchi said the Ebola outbreak had highlighted the need for rules on clinical research to be broken sometimes.
He said: "In dealing with the deadly Ebola outbreak, the World Health Organisation has decided that departure from standard evidence-based treatment is fully justified and essential.
“It has set ethical guidelines for the use of new therapies and interventions - they are identical to the provisions of the Medical Innovation Bill.”
GMC chairman Professor Peter Rubin told the paper: "While we welcome the amendments to the Bill in Lord Saatchi’s name, we look forward to seeing the final version."
According to Demos, nearly 100,000 undocumented migrants avoid using NHS services or seeing a GP.
They fear this may lead to their discovery or to their incurring charges as the government cracks down on alleged health tourism, the think-tank warns.
The government dropped plans to require GPs to levy fees on migrants - but is putting other measures in place to recover NHS costs from travellers from overseas.
The report says: "It would be short-sighted to allow the important task of protecting the NHS from fraud to expose the British public to increased risks stemming from communicable disease."
Researcher Max Wind-Cowie told the Independent on Sunday: "The current Ebola outbreak puts this issue in extremely sharp focus."
A Department of Health spokesman said: "The NHS is there to care and support people who are unwell, but we must ensure it is funded fairly.
"We are working closely with representatives of vulnerable groups to make sure migrants know that urgent treatment will always be provided regardless of their ability to pay."
Hungarian researchers say they have pinned down the relationship of the season of birth to human temperament.
Many people have long believed that the date and time of birth influence character.
The latest study has linked four types of temperament to the four seasons.
The researchers studied some 400 people and reported their findings to the conference of the European College of Neuropsychopharmacology in Berlin, Germany.
This linked the cyclothymic temperament - affected by mood swings - to summer birth.
Hyperthymic people - who are excessively positive - can be born in both the spring and the summer, the researchers found.
Meanwhile winter babies tend to have a more cheerful and less irritable personality than others.
But, according to the researchers, they are still more prone to depression than autumn babies.
Researcher Professor Xenia Gonda, from Budapest, said the season of birth could influence the level of brain chemicals such as dopamine and serotonin.
Professor Gonda said: "Basically, it seems that when you are born may increase or decrease your chance of developing certain mood disorders.
"We can't yet say anything about the mechanisms involved. What we are now looking at is to see if there are genetic markers which are related to season of birth and mood disorder."
Professor Eduard Vieta, from the College, said the study of the seasons gave new insights into temperament.
He said: "Temperaments are not disorders but biologically-driven behavioural and emotional trends. Although both genetic and environmental factors are involved in one's temperament, now we know that the season at birth plays a role too.
"And the finding of 'high mood' tendency (hyperthymic temperament) for those born in summer is quite intriguing."
A new study highlights parts of the country with the highest death rates from the problem.
Increasing rates of liver disease have been driven both by alcohol use and by the spread of hepatitis viruses. Experts say obesity is also a major factor.
The Public Health England study shows the highest death rates in Blackpool - more than four times rates in central Bedfordshire.
The organisation says that death rates have increased by 40% this century. In 2012, some 10,948 deaths were linked to liver disease.
Professor Julia Verne, the organisation's liver disease specialist, said: “Liver disease is a public health priority because young lives are being needlessly lost. All the preventable causes are on the rise, but alcohol accounts for 37% of liver disease deaths.
"We must do more to raise awareness, nationally and locally, and this is why it is so important for the public and health professionals to understand their local picture.”
Andrew Langford, of The British Liver Trust, welcomed the publication of the district-by-district analysis of liver disease.
He said: "These profiles, which were urgently needed, will begin to address the devastating rise of poor liver health throughout the country and reduce unnecessary deaths of increasingly younger people from liver disease."
The regional analysis of liver disease rates is due to be published at [Profiles]