One of two men arrested in the immediate aftermath of the murder and released without charge, he is now believed to have gone into hiding, possibly in the Republic, The Sunday Times reported.
Ms McKee, a 29-year-old journalist, died after she was shot while observing dissident republican rioting in Creggan on Thursday, April 18.
The New IRA later admitted responsibility for the murder.
According to police, 18 searches have been carried out in connection with the wider investigation into Ms McKee’s death.
Nine people have been arrested and two are facing charges linked to the riot following the night of violence.
No one has so far been charged with Ms McKee’s murder.
CCTV footage of the murder shows a masked man firing shots from behind a wall, while an accomplice collects the used bullet cases.The pair wore masks and distinctive clothing, but forensic analysis of the footage has not secured a positive match with those the police believe are responsible.
Detective Supt Jason Murphy has repeated an appeal for information, reminding witnesses that the matter will be dealt with sensitively.
He said: “I recognise people living in Creggan may feel it’s difficult to come forward to speak to police.
“I want to provide a personal reassurance that we are able to deal with these concerns sensitively.”
Independent charity Crimestoppers has offered a £10,000 reward for information leading to the arrest and successful prosecution of those involved in Ms McKee’s murder.