Other relatives are understood to have raised the alarm. Both the children's parents are from Somalia, although the children were born in Manchester.
Police say the trio may be living in the Somali community in Birmingham or London or could even have left the country. Detectives are checking airport records to establish their whereabouts.
Det Insp Kevin Marriott, investigating, said: "We are appealing to the Somalian community to come forward with any information on their whereabouts.
"Although they could have left the country, it is also possible that they could be in other areas."
Anyone with information is asked to contact police on 8725050 or Crimestoppers, anonymously, on 0800 555 111.
Source: Manchester Evening News