The deaths happened at Stepping Hill Hospital in Stockport, near Manchester.
The Guardian newspaper said tests were being carried out to determine if a saline solution injected with insulin was "directly responsible" for the deaths of Tracey Arden, 44, George Keep, 84, and Arnold Lancaster, 71.
And autopsies were to be carried out on an 84-year-old woman and an 83-year-old man, who both died with low blood sugar levels, the paper said.
Insulin prompts the body to absorb glucose, a form of sugar, from the blood; if severe enough, this condition can lead to death.
The Guardian newspaper also said a man in his 40s was in critical condition in a hospital after a surprise drop in his blood sugar levels.
The Guardian reported that the nurse, Rebecca Leighton, 27, was arrested at her home in Heaviley, Stockport, on Wednesday. She was being questioned by police on suspicion of murder, but had not been charged.
Police are looking into the treatment of 14 patients since July 7, the paper reported. It said 36 bags of saline were found to have been sabotaged with insulin.
The Telegraph newspaper's website quoted Valerie Rowlinson, a friend of Leighton, as saying she was shocked at the arrest.
"Becki always wanted to be a nurse like her mother," she told the paper. "She was very dedicated and a very hard worker. I always found her extremely committed and diligent, she was a good nurse in my opinion."