Despite the best efforts of medical staff, the baby, who has since been formally identified as Felicity-May Harvey, sadly passed away on Monday 11 January.
Police said a 24-year-old man was arrested on suspicion of murder and has since been released on bail pending further enquiries.
Paying tribute to Felicity-May, the Harvey family said: "Our hearts are broken after losing our precious baby girl, Felicity-May. She was a gorgeous baby and always so alert, looking around with her big blue eyes.
"She was absolutely beautiful and incredibly brave and she melted the hearts of everyone who met her. What made her extra special was her cleft lip and palate, and despite the challenges of this she was the most happy and content little girl.
"She was and always will be loved by her mum, sisters and family and there is a huge void in all our hearts and lives now that she has been taken from us.
"She was our special star, and it is not fair that she shone brightly for only a short time. When we look up at the sky, we will look through the clouds and know that the brightest star shining is our Felicity-May.
"Rest in peace baby girl. Sleep tight. Until we meet again, our precious angel."
Earlier this week a pink banner with the words 'baby girl' was fixed to the front door of a house on Stirling Place where paramedics called police after having concerns about the baby.
Floral tributes had also been left at the scene.
Detective Chief Inspector Carl Jones, of GMP's Major Incident Team, said: "This is a desperately sad incident where a baby girl has lost her life and we are doing what we can to support her loved ones at this incredibly difficult time.
"Our investigation is ongoing; as always, we are keeping an open mind and have specialist officers working at the scene and on the investigation to establish the full facts of this case.
"This is a heart-breaking time and we ask the public to refrain from speculation and respect the family's privacy at this time.
“Anyone with information should do the right thing and contact us with information so we can continue to try and ascertain the circumstances behind this tragedy.”
Anyone with information should call police on 0161 856 3400 quoting incident 1896 of 08/01/2021. Details can be passed anonymously to the independent Crimestoppers on 0800 555 111.