The woman - who is in her 40s - left the address about 5.45am and walked a short distance before knocking on a door of a house to ask for help.
A man answered and called her a taxi which took her back to the Fallowfield area.
Officers have been carrying out extensive enquiries and have now released CCTV images.
Detective Constable Julie Tsang, from GMP's Salford borough, said:
"We are keen to speak to the man pictured and anyone who recognises him.
"If you think you might know who he is, or this is you, then please contact us immediately.
"We would also like to speak to the man who helped the victim get a taxi.
"I want to stress you are not in any trouble, but you might have information which could really help this investigation.
"Anyone who has any information is urged to call us."
Details can be passed on by calling police on 101. Alternatively, information can be passed on anonymously by contacting Crimestoppers on 0800 555 111.