Fourteen people were selected Monday to be among the 12 jurors and six alternates after nine hours of interviewing potential jurors one by one. The last four panelists are expected to be selected Tuesday.
William Balfour is accused of killing Hudson's mother, Darnell Donerson, 57; brother Jason Hudson, 29; and 7-year-old nephew Julian King in Chicago in October 2008. Prosecutors said Balfour shot the family members in a jealous rage because his estranged wife and the singer's sister, Julia Hudson, was dating another man.
Balfour, 30, faces a maximum sentence of life in prison if convicted.
Cook County Circuit Judge Charles Burns has said he'd like a full jury in place by Wednesday. Burns will aim to weed out those who may be swayed by 30-year-old Hudson's celebrity. But he's not likely to automatically exclude fans if they can convince him that their biases won't affect deliberations. Burns told would-be jurors that anyone opposed to capital punishment need not worry because Illinois abolished the death penalty last year.
One woman in her 30s, a salesperson at Xerox, was dismissed after she told those assembled in the back room, including Balfour, that she is a big fan of Hudson's and would be unable to discount the tragedy and give the defendant a fair trial.
"I'm a fan of Jennifer Hudson's and I feel bad for what she went through," she said.
Only a few people said they knew little to nothing about Hudson. One women in her 30s picked for the jury said she had heard of Hudson but had no idea what she looked like.
Balfour's lawyers have said the evidence is circumstantial. But prosecutors say the proof includes gun residue found on his car's steering wheel, and that testimony will show he lied about his whereabouts the day of the murders.
The Oscar winner is expected to be in the courtroom every day and could testify. Testimony in the case begins April 23.
The Associated Press contributed to this report.