Butt and Amir's appeal to be heard on Nov 23
Butt was given a two-and-a-half year jail term after being found guilty of conspiracy to cheat and conspiracy to accept corrupt payments based on orchestrating no-balls against England, at Lord's, in 2010.
Amir was given two six-month sentences under the same charges, to run concurrently, and is currently in detention at a young offenders' institute.
The Court of Appeal will hear their cases on Wednesday and it will be presided over by the Lord Chief Justice.
Mohammad Asif and agent Mazhar Majeed were jailed for a year and 32 months respectively. The three cricketers and Majeed were caught after a News of the World sting operation which produced evidence of Majeed setting up the deliberate no-balls that were delivered during England's first innings at Lord's. Majeed claimed to have paid Asif £65,000, Butt £10,000 and Amir £2,500.