He said he had received information that a woman posted on Facebook that her hairdresser had inside information from a juror about how deliberations were going before the verdict was reached.
In a letter to SBI Director Greg McLeod, Stephens said such gossip is usually baseless, but should be investigated.
Meanwhile, a juror who decided Young's fate thinks the allegations of jury misconduct are untrue,
"Honestly, I think it's a rumor someone threw out there," said jury foreperson Tracey Raksnis.
Raksnis thinks the allegations of jury misconduct are ridiculous. However, she admits she only knew her fellow jury members so well.
"You don't know what facade people put on and what they say behind closed doors," said Raksnis. "It's a shame and I feel heartbroken if this is true."
Still, Raksnis is sure none of the jury members did anything wrong.
"Oh, I can assure you and whoever else is paying attention that there was never a not guilty," said Raksnis. "We were always at six guilty, six undecided. I feel with a thousand percent that all of us understood the gravity of the situation and understood what we had to do."
The allegations came one day after Young, 37, was convicted and sent to prison for life in the 2006 beating death of his wife Michelle.
Michelle was five months pregnant when she died in the couple's south Raleigh home. The Young's daughter Cassidy - who was 2-years-old at the time - was found unharmed next to her mother's corpse. Investigators said her tiny bloody footprints were tracked throughout the upstairs floor of the home on Birchleaf Drive.
Monday's guilty verdict was the prosecution's second attempt to put Young behind bars. His first trial ended with a deadlocked jury last year.
Legal experts told ABC11 Tuesday that a possible second mistrial would depend on the seriousness of any juror misconduct if it's found to be true.