The abuse took place while the boys were living at Belmont House, in Baker Street, Stockport, Greater Manchester, in about 1989 and 1990.
The home, which was also known as Belmont Assessment Centre, has closed.
Police have made "extensive" inquiries and are now appealing for anyone who worked or lived at the home during that period to contact them.
Det Con Karen Wileman said: "People who were previously residents or members of staff at the home may have moved to different areas of the country, or even abroad.
"We are keen to speak to anyone who was involved with the home around the time the abuse took place."
An appeal has been launched after two boys were sexually abused at a former care home.