The top court will hear from Raffaele Sollecito’s defense team on March 27 before the judges give their verdict.
Former lovers Amanda Knox and Raffaele Sollecito were convicted for the second time in 2014.
They have maintained their innocence throughout and have already served four years in prison.
The Court of Cassation in Rome is due to confirm the guilty verdict or overturn it – either ordering another trial or effectively bringing about an acquittal.
A definitive conviction would trigger complicated attempts to extradite American Knox, who lives in Seattle in the US.
Raffaele Sollecito, from Bari, southern Italy, has remained in the country, and attended the court with his new girlfriend on March 25.
Speaking before the hearing, the Kercher family’s lawyer, Francesco Maresca, said they hoped the court’s decision would bring an end to the judicial process.
“It’s a case that has gone on for so many years now,” he said.
“They hope that this will be the final stage of this judicial process and they will at last… be able to remember Meredith outside of the court room [process].”
Leeds University student Meredith Kercher, 21, from Coulsdon, south London, was found dead in the flat she shared with Amanda Knox, now 27, in Perugia, central Italy, where both women were studying.
Amanda Knox and Raffaele Sollecito, 30, were convicted of the murder by a trial court in Perugia in 2009.
They were freed in 2011 after an appellate court overturned the convictions.
The Court of Cassation rebuked the appellate judge’s reasoning and last year an appeals court in Florence sentenced Amanda Knox to 28 years and Raffaele Sollecito to 25 years.
The latest ruling could confirm that conviction or overturn it – and either order yet another trial or effectively acquit the pair, although legal experts say the last option is unlikely.
Rudy Hermann Guede, born in the Ivory Coast, who opted for a fast-track trial, is serving a 16-year sentence for his role in the murder of Meredith Kercher.
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