An application has been made for the hearing at the court of appeal, but no date has been set.
Bennell, 64, was sentenced for 50 child sex offences against 12 young boys between the late 1970s and early 1990s.
During his six-week trial, the court heard evidence of “industrial scale” abuse committed by Mr Bennell against vulnerable boys in his care.
The former coach, who had worked for Manchester City and Crewe Alexandra, was sentenced at Liverpool Crown Court.
Shame and fear meant many of the paedophile’s victims – who said the coach had a “power hold” over young boys who dreamed of becoming professional footballers – took decades to come forward.
During sentencing, Judge Goldstone said Bennell’s abuse had led to suicidal thoughts, depression and alcoholism among his victims, and called the former coach the “devil incarnate”.
Bennell has previously served three jail terms totalling 15 years, for similar offences.
Cheshire police continue to investigate his case, believing there may be more than 100 victims in total.
Eleanor Laws, his lawyer, argued Bennell was on anti-anxiety medication and has suffered from cancer, and said his time in custody would be “less comfortable and more difficult” than somebody without these conditions.