Quebec Superior Court Justice Guy Cournoyer said he'll decide whether to OK the request, which would entail taking evidence from witnesses who don't actually attend a Canadian court.
Magnotta's trial in the May 2012 death of Concordia University student Jun Lin is scheduled to take place this coming September.
Magnotta, 31, left Canada after the alleged murder and went to France and then Germany, where he was arrested in June 2012.
The accused, who appeared in court Thursday wearing a black T-shirt with a picture of Marilyn Monroe on the front, listened impassively as he heard the Crown outline its reasons.
Prosecutor Louis Bouthillier said the Crown wants to interview more than 30 witnesses in France and Germany and that bringing them across the Atlantic would be a logistical nightmare.
The planning behind taking evidence abroad and ironing out all the details could take between four and six months to complete.
Magnotta's first-degree murder trial is set to begin Sept. 8 and last between six and eight weeks. He has pleaded not guilty to the charges he faces.
"If they don't show up come September, we're stuck between a rock and a hard place," Bouthillier said.
While a Montreal police investigator confirmed they spoke to some witnesses during a trip to Europe last April, they have yet to do an exhaustive questioning of most.
The process of collecting testimony abroad is wrought with technological and jurisdictional hurdles.
Sebastien Bergeron-Guyard, a prosecutor who deals with international cases involving Quebec, said many courtrooms in France and Germany are not equipped with audio and video equipment to record testimony.
He also said there is no legal way to compel witnesses from a foreign country to testify in Canada.
And there are differences in the way legal systems work abroad. There are no cross-examinations in French and German courts, which abide by a different legal tradition.
Magnotta's attorney, Luc Leclair, said the witnesses should be brought to Canada on the federal government's dime.
Barring that, Leclair believes the witnesses should appear by video conference. Gathering of testimony abroad should be a last resort.
As for Magnotta attending any European hearings, Bergeron-Guyard said it would be highly unlikely.
"When we move someone out of Canada, we're never sure we'll have them back because we don't have jurisdiction anymore," he said.
"If we move them, we have to start the extradition process anew, so we're never sure if we'll get them back."
Leclair said his biggest concern is that Magnotta will be unable to attend such hearings and might be unable to participate in the process.
"My first position is that he should be here, the trial should be here and the witnesses should be here," he said.
Leclair pegged the cost of bringing Magnotta back to Canada at $450,000 and said if authorities did it once, they can do it again to bring witnesses here.
"If Mr. (Prime Minister Stephen) Harper was able to pay $450,000, they can pay to have 20 to 35 witnesses to come to Canada," Leclair said.
The Canadian Press reported in September 2012 that the cost of extradition from Germany, aboard a government plane fit for the prime minister, was expected to be about $375,000. It's not clear how much the Montreal police spent on their end.
Several other motions relating to the case are expected to be dealt with on Friday.