Sophie Jones was rushed to hospital from her home in Blackpool on Tuesday night after reportedly suffering a cardiac arrest. She later died at Blackpool Victoria Hospital.
Detective Superintendent Paul Withers, of Lancashire Police, said he believed methadone - a heroin substitute used by drug addicts - was removed from the house after the incident.
Sophie died after an ambulance was called to an address in Jameson Street at about 11.45pm on Tuesday.
A 29-year-old woman and a 41-year-old man, from Blackpool, continue to be questioned on suspicion of child neglect, manslaughter and attempting to pervert the course of justice.
"We are pursuing numerous lines of inquiry as we try to establish the circumstances surrounding Sophie's death," said Detective Superintendent Withers. "One line of inquiry is that she may have ingested methadone. However, at this stage we cannot categorically say that this is the case or that it has caused her death.
"If anybody has any information which they think could be relevant to this inquiry then I would urge them to contact police.
"This is a tragic incident where a little girl has lost her life and I am determined to get to the bottom of what happened to Sophie Jones.
"As a result of our inquiries, I believe that a substance was removed from the address on Jameson Street either shortly before paramedics arrived or after, and I believe that substance to be methadone.
"I believe it is either being held by someone locally or has been hidden somewhere in the vicinity of Jameson Street. If anybody has any information relating to where it is then I would urge them to come forward.
"Methadone is green in colour and in this instance may not necessarily be in a clearly identified medicine bottle.
"If this substance fell into the wrong hands it could have incredibly serious consequences. I would like to reassure people that any information which is passed to us will be treated in confidence."
A post-mortem examination has been carried out but the cause of Sophie's death has not been determined and further toxicology tests will now be carried out.
Anybody with any information can contact police on 101 or Crimestoppers anonymously on 0800 555 111 or online at Crimestoppers-uk.org.