The University of Leicester has not ruled out the possibility that the remains of Richard III will be put on public display.
According to the Ministry of Justice, the skeleton, which was uncovered in August, is in the care of the university.
It is expected to be reinterred at Leicester Cathedral next spring.
However, before the official re-burial, the remains are being kept at the university, which said it had not made a decision on whether or not to allow the public to see them.
Richard Taylor, deputy registrar and director of corporate affairs, said: "We need to balance legitimate public interest with a requirement to protect dignity."
A spokeswoman for Leicester Cathedral said it was up to the university, but the church would not take part in any public showings.
She said: "Scientists may have a reason for seeing them, but that is different from public display in the cathedral."
Leicester City Council's Richard III museum, which will be built at the former Leicester Grammar School, near the Greyfriars site, would be an obvious place for the remains, mayor Sir Peter Soulsby said.
However, he said he understood the need for a respectful reinterment.
Following the press conference announcing the remains were of Richard III, members of the media were allowed to view the skeleton in small groups, in silence, under the gaze of a member of the clergy.
Sir Peter said: "I think the arrangements made for the press to see the remains were a model of how to do it effectively, but with dignity.
"If they are going to be displayed then the university would want to take a similar approach.
"The public interest in this project has been phenomenal, but I don't think politicians have a place in this sort of decision."
Sir Peter said the centrepiece of the museum display would be a replica skeleton, created using CT scans and three-dimensional printing techniques at Loughborough University.
Professor Russell Harris, from the university, said: "There are a lot of different and exciting opportunities we could pursue regarding the remains.
"We've recreated the skull and the next obvious thing is a replica skeleton.
"We have the tools at the university so once a final decision about the project has been made, it should be pretty straightforward."
Prof Harris said he would discuss the matter today with Dr Jo Appleby, from the University of Leicester.
The recreated skeleton would join the University of Dundee's facial reconstruction model, which is expected to be on permanent loan when the permanent museum opens next year.
