Federal prosecutors normally have 30 days to file an indictment against a defendant. That deadline is Jan. 7; an extension, if granted, would give prosecutors until April 7 to indict the governor.
Blagojevich was arrested on Dec. 9 on a criminal complaint that he tried to sell President-elect Barack Obama's vacant U.S. Senate seat to the highest bidder. Blagojevich, who on Thursday named former state Attorney General Roland Burris to replace Obama, has denied any wrongdoing.
In a five-page motion submitted to the court Wednesday, Fitzgerald said the holiday season has limited the dates and times that the prosecutors have been able to present evidence to a grand jury.
The prosecutor said "multiple witnesses" have come forward in recent weeks and investigators have to review "thousands of intercepted phone calls."
Given the volume of evidence involved, he said, 30 days was insufficient.
"The investigation includes multiple defendants and potential defendants as well as thousands of intercepted phone calls, and additional factors warranting an extension of time," he wrote.
"The government cannot complete its investigation and appropriately conclude the investigation within the time allowed under The Speedy Trial Act," the motion continues.
In the final page of the motion, Fitzgerald wrote that pursuant to phone calls and meetings "over the past week," Blagojevich's attorney indicated he does not object to the motion.
This motion will be presented before Chief Judge James Holderman on Monday afternoon. George Washington University law professor Jonathan Turley said he expects Fitzgerald will be granted the motion in spite of his actions.
"I'm surprised by it, because at the press conference, he made this out to be the world's strongest criminal case," Turley told FOXNews.com, adding that he thought Fitzgerald acted rather cavalierly at the Dec. 9 press conference by raising the bar so high in claiming Blagojevich was so corrupt.
"I think most judges would be put out by Fitzgerald's conduct," he said.
FOX News' Lee Ross and The Associated Press contributed to this report.