Rudy Guede, 22, was jailed for 30 years for knifing and sexually assaulting the 21-year-old victim at her home in Perugia, Italy, in 2007.
Appealing against his conviction, the drifter told a court he saw American Knox's "silhouette" running away from the house after he found the Briton dying, Sky News reported.
Guede added that he had ''not raped or killed'' Meredith and apologized to her family for not doing enough to save the student after her throat was slashed, the Web site reported.
Ivory Coast-born Guede was sentenced in October 2008 following a fast-track trial.
His appeal is being heard just two days before the murder trial of Knox, 22, and her former boyfriend, 25-year-old Italian Raffaele Sollecito, resumes.
In a statement to the court in Perugia, Guede told how he met Meredith at a Halloween party in October 2007 and visited the house she shared with Knox the next day.
He said Meredith started complaining about cash going missing and blamed Knox, saying: "My money, my money. I can't stand her (Knox)," Sky News reported.
Guede said he went to the bathroom and put on his Ipod, but soon heard the two women shouting, then by "a loud scream."