Three judges at the Court of Appeal in London will hear challenges by Kevin Liverpool and Junior Bradshaw.
The pair were found guilty of conspiracy to murder and conspiracy to rob following a three-week trial at Exeter Crown Court last year.
Liverpool was given a life sentence, with a minimum term of 10 years and eight months, while Bradshaw was jailed for 18 years.
The pairs were arrested near the star's home in Cullompton in June 2011.
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