Homosexual men in Britain can donate blood only if they have abstained from sex for a decade.
The ban is being lifted after it was decided that it could be discriminatory and might breach equality legislation.
The changes are expected to be announced by Anne Milton, the public health minister, and she is understood to be backed by Andrew Lansley, the Health Secretary, and Lynne Featherstone, the Equalities Minister.
The current system is based on trust. There are no checks to ensure donors are telling the truth about their sexuality and around seven percent of sexually active gay men are thought to give blood despite the ban.
The changes were instigated by Sabto, the advisory committee on the safety of blood, tissues and organs, which had concluded that if the ban were replaced by a new rule preventing gay men from giving blood for five years after having sex with another man, the risk of HIV reaching the blood supply would go up by less than 5 percent.
It is estimated that this figure would halve if the "deferral" period were increased to 10 years, so ministers backed this option.
The 10-year delay also ensures that people who are not aware they have contracted HIV do not pass it on accidentally.
"A complete ban is unfair and discriminatory but we need to protect public health, so the 10-year rule is what is being considered," the Telegraph quoted a Government source as saying.
According to the Terrence Higgins Trust, the HIV charity, about 42 percent of people infected with HIV in 2009 were homosexual men, and there are an estimated 86,500 people with HIV in Britain, with a quarter unaware that they have an infection.
Gay rights campaigners have pushed for the ban to be lifted, saying many homosexual men are in long-term monogamous relationships, practise safe sex or have been celibate for years.