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.
Man on a mission to bring Plymouth alive at night
Lack of things to do after 7pm
Quick build homes not so swift
Delays hamper completion in Mid Devon village
New gadget to thwart Paignton seafront car pests
Anti-social driving has been blighting the area for some time'
East Devon cliff fall site still under scrutiny
The fall at Beer has been investigated
Exeter's new waste recycling plant to cost £13 million
New building will be cheaper than modernising existing plant
