Ms Dornan died on Sunday 2 August. She had been stabbed before her home, in the Lagmore estate, was set on fire.
Sources have told the BBC that the 37-year-old suspect, who was arrested by Irish police (Garda??) in County Donegal on Friday, had absconded a month ago.
The Police Service of Northern Ireland is considering seeking his extradition.
Following the man's arrest, a PSNI spokesperson said they were no longer looking for anyone in connection with the murder.
A suspect in the murder of west Belfast woman Jennifer Dornan had failed to return to Dublin's Mountjoy prison after a temporary release.