Liang's lawyers argued that Michael Vargas "lied to the court... when he reported that no one in his 'close family' had been accused of a crime," according to the motion, adding that Vargas' father spent seven years in prison for accidentally shooting a friend.
Liang was convicted in February of manslaughter for accidentally shooting an unarmed man in a housing project.
A New York Daily News report from March said that an unnamed juror, later identified as Vargas, was among a group of jurors that "expressed shock and dismay," that the Brooklyn District Attorney recommended no jail time for Liang.
During jury selection, the court asked Vargas whether anyone close to him has been convicted of a crime, to which he responds "none that have made the papers, I don't think," records show.
When he is pressed, Vargas tells the court "no, no."
"Although the Court need not determine that Mr. Vargas was actually biased, his comments to the Daily News indicate that he was," the motion says.
Juror: Lawyers are 'grabbing at straws'
Vargas told CNN on Tuesday that he is not biased and that Liang's lawyers are "grabbing for straws, hoping that the rain falls into their bucket."
"He is my father, but he didn't raise me. I didn't live with him, and I didn't know him," Vargas said. "He is nothing to me; that's why it never came to me. That idea never crossed my mind."
Liang's lawyers also included Facebook posts by Vargas, which they say indicate his bias against police officers.
He reiterated that he isn't biased, and he has police officers in his family, which he says he told the court during jury selection.
"All I do is repost what somebody else said. That's all it is. They're going to make anything they can out of it," Vargas said of the Facebook posts.
His "dismay" to a recommendation of no-jail sentence had nothing to do with his father, he said.
"Why did they try so hard for a conviction to give them a slap on the wrist? When you take somebody's life, to me, that is the worst crime. I understand it was an accident, that's why it's not murder," Vargas said.
He said that he is willing to appear before the judge if it comes to it.
"At this point, I only want to defend myself to a judge. I want to speak with him and explain myself."