Prosecutor Alessandro Crini made the request after two days of closing arguments in the third trial involving the violent, sex-charged murder of Meredith Kercher.
Knox was sentenced to 26 years in the first trial, including one year for slander for blaming Kercher's murder on a Congolese-born bar owner.
The appeals court that overturned the murder conviction confirmed Knox's slander conviction and raised the penalty to three years. When she was released after the appeal, Knox had already served four years, which covered her slander sentence.
Crini also demanded 26 years for her co-defendant, Raffaele Sollecito.
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