Rudy Hermann Guede, who is from the Ivory Coast, was convicted of killing the 21-year-old in Perugia, Italy, where she was sharing an apartment with US student Amanda Knox.
Guede, now 29, is currently serving a 16-year sentence in an Italian prison for the murder but has always denied killing Miss Kercher.
Italian media claim that his lawyers filed a request to have his conviction overturned on Tuesday, while stating that their client is innocent.
Guede’s conviction ruled he committed homicide “acting with others”, but he is the only one to be definitively convicted of the murder.
Miss Kercher, an exchange student from Coulsdon, Surrey, was discovered with her throat cut in the bedroom of her apartment in Perugia on November 2 2007.
Her body was partially clothed and under a duvet, and a post-mortem examination showed evidence of sexual activity at some point before her death.
It is unclear if a new trial for Guede could be granted due to the fact that he has exhausted his appeals.
Miss Knox and her then boyfriend Raffaele Sollecito, who steadfastly proclaimed their innocence over several years, were acquitted last year by Italy’s highest criminal court.
However, the court did uphold her slander conviction for wrongly accusing bar owner Diya Lumumba in the murder. It reduced that sentence to three years.
Miss Knox spent nearly four years in jail after being convicted of the brutal murder and sexual assault of Miss Kercher. She had been sentenced to 26 years in her initial trial.
During a seven-and-a-half year court battle, she returned to the United States after being acquitted only to face another trial after the acquittal was thrown out.
She then faced her second appeals trial and high court proceedings in absentia while living in Washington.