Sampieri punched, bound and choked the girl for almost an hour while he filmed part of the ordeal and threatened to kill her at Kogarah in November 2018.
Sampieri pleaded guilty to 10 charges related to the attack and was sentenced to life in jail with no non-parole period in the NSW District Court on February 12.
The rapist also admitted to charges related to 94 sexually explicit and harassing phone calls he made to women in the months before the attack.
The 56-year-old has liver cancer and only a few years to live, and will spend the rest of his life behind bars.
He lodged a notice of intention to appeal with the NSW Court of Criminal Appeal one day after his sentencing.
Sampieri must outline his case for appeal by August 13.
His lawyer, Penny Musgrave, confirmed to AAP on Wednesday that Sampieri had lodged the notice of his intention to appeal, which gives him six months to decide whether he will go ahead with it.
Sampieri, who was on parole at the time for an earlier rape in Wollongong, was high on ice during the attack on the child.
Acting Judge Paul Conlon in sentencing said the attack could “only be described as any parent’s worst nightmare”.
He said it would have been terrifying and the girl would have held “grave fears” for her life.
The judge described mechanic Nick Gilio as brave for confronting the knife- wielding Sampieri after he found the girl in the toilets.
Mr Gilio suffered several large cuts during the confrontation, including a 14cm wound to the back of his head and cuts to his neck and abdomen.