In a memo to U.S. District Judge Dale Kimball, the prosecutors oppose the defense request to move Brian Mitchell's trial out of state, The Salt Lake City Tribune reported.
Mitchell's trial is to begin Nov. 1.
Smart, 14 at the time, disappeared from her home in Salt Lake City in 2002. In March 2003, nine months later, she turned up in Sandy, Utah, less than 20 miles away, with Mitchell and his wife Wanda Barzee.
Prosecutors said 99 percent of the potential jurors said in questionnaires that they had seen news coverage about the case but only 24 percent said they would be biased against Mitchell by media reports.
"A vast majority also reported some skepticism about the accuracy of news reporting," prosecutors added.
Barzee pleaded guilty and is serving a 15-year term. Kimball found Mitchell competent to stand trial in March after years of delay.