Theresa May will say next week she plans to introduce "Clare's Law" in four areas for a year, before extending it across England and Wales.
Mrs May is thought to have decided to give women - or men - the right to ask police about a partner's history.
A tougher option, to give an individual or their friends and family a right to demand them information from police, is thought to have been rejected.
The legislation has been named after Michael Brown's daughter Clare Wood, a 36-year-old mother strangled and set alight by a boyfriend she met on Facebook.
Mr Brown began his campaign to change the law six months ago, and has been contacted by countless women experiencing domestic abuse.
Ministers now want women like Clare, and men, to be able to go to police to check out a partner's history.
One of the trials will be in Salford, Manchester. Local Labour MP Hazel Blears told Channel 4 News said it was "incredibly important".
Domestic violence is on the increase, with 21 men and 94 women murdered by a partner, ex-partner or lover in 2010 - more than two a week.
A Home Office spokesman said: "Domestic violence is a particularly dreadful form of abuse and we are constantly looking at ways to strengthen protection for victims.
"That is why we consulted on introducing a domestic violence disclosure scheme, often known as 'Clare's law'. We will be making a formal announcement shortly."