Hadeer Jamil Alonazi, 26, from Rusholme, South Manchester was reported missing on July 2.
Police say Hadeer and her six-year-old daughter, originally from Kuwait and members of the Bidoon Arab minority, had travelled to the UK in November 2018 from Mitilini, on the Greek island of Lesbos and were welcomed as refugees.
GMP have now confirmed they have received a missing from home inquiry and can therefore not 'exclusively treat' the case as a 'murder inquiry'.
Detective Chief Inspector Liz Hopkinson, of GMP's Major Incident Team, said:
We are very concerned about her and fear she may have come to some harm. The inquiry is being treated as a murder inquiry, but at the same time we have a missing from home inquiry.
DCI Hopkinson added: "It is a sensitive inquiry. We have got a lot of inquiries going on, but we do need help. I would ask anyone who believes they may have seen something suspicious that may be linked to Hadeer's disappearance to come forward.
"Inquiries suggest that Hadeer was living at the property in Hall Road up until June 2019."
I am asking anyone who lives in the Rusholme community or beyond who knows where she is or what has happened to her to come forward and help find her.