Archaeologists are looking into the possibility that the second set of human remains found at the Richard III dig site are those of the friary's founder.
A female skeleton was unearthed at the Franciscan friary in the city centre at the same time as University of Leicester scientists were excavating the body of a man they believe could be Richard III.
The female remains have not been subjected to the same rigorous examination as those of the last Plantagenet king.
However, evidence suggests they may be the remains of Ellen Luenor who, along with husband Gilbert, is thought to have founded the 13th century friary now buried beneath the Greyfriars car park, in New Street.
Dig site manager Mathew Morris said: "The remains were found in the east end of the church and there's a possibility they belong to Ellen Luenor, who could be either a benefactor or the founder of the friary where Richard may be buried.
"We haven't had the chance to get into any detailed analysis of the remains, but it is something that we would like to do in the near future."
The resting place of the female skeleton was in a different part of the friary to the supposed grave of Richard III.
Richard Buckley, co-director of the university's archaeology service, said that at some point the bones had been reburied.
He said: "It wasn't a full skeleton.
"It's not uncommon. When we excavated the area beneath the John Lewis car park we found stacks of bones neatly stored on top of each other."
Archaeologists believe the skeleton may have been dug up by a gardener when the site was the garden of a mansion house in the 17th century. Mr Morris said: "They were buried at a higher level than the church floor and the bones were not intact, which suggests that someone dug them up by accident and reburied them in a different spot, just not as deep."
University of Leicester academics will examine the bones once they have been able to establish whether or not the male remains are those of Richard III.
Any identification of the former king's body is at least two weeks away, with the results likely to be released in the new year.
DNA from the 500-year-old bones are being tested against genetic information gathered from descendant Michael Ibsen, a Canadian-born furniture maker now living in London.
A Channel 4 documentary, which followed the University of Leicester dig team during the excavation, will air in January.
