Aaron Campbell was convicted at the High Court in Glasgow last month where a jury found him guilty unanimously following a nine-day trial.
The 16-year-old abducted, raped and murdered the youngster and been locked up for at least 27 years.
Alesha’s body was found in woods on the Isle of Bute on July 2 last year, hours after she was reported missing from the house her father shared with his parents and partner on the island
The girl was days into her summer holiday with father Robert MacPhail, 26, and grandparents Angela King and Calum MacPhail when she was snatched by Campbell, who tried to blame her father’s girlfriend Toni McLachlan, 18, for the crime.
A spokesperson for the Scottish Courts and Tribunals Service said: “We can confirm a note of appeal has been lodged.”